arrays of gold nanoparticles as a platform for molecular ... · 5.3 from a double junction to an...

Arrays of gold nanoparticles as aplatform for molecular electronics

Inauguraldissertation

zurErlangung der Würde eines Doktors der Philosophie

vorgelegt derPhilosophisch-Naturwissenschaftlichen Fakultät

der Universität Basel

von

Jón Skírnir Ágústssonaus Reykjavík (IS)

Basel, 2011

Genehmigt von der Philosophisch-Naturwissenschaftlichen Fakultätauf Antrag vonProf. Dr. Christian SchönenbergerDr.ir. Sense Jan van der MolenDr. Aidan QuinnDr. Michel Calame

Basel, den 13. Mai 2011

Prof. Dr. Eberhard ParlowDekan

An expert is a man who has made all the mistakeswhich can be made in a very narrow field.

Niels Bohr

Contents

1 Introduction 1

I Nanoparticle arrays as a platform for molecular devices 3

2 Device fabrication 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Preparation of Au nanoparticles and Au nanoparticle arrays . . . . . . 62.3 Au nanoparticle arrays as a platform for molecular electronics . . . . 8

3 Adding function to nanoparticle arrays 113.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Controlling the oxidation state of a redox–active molecule . . . . . . 123.3 Introducing function to the nanoparticle arrays . . . . . . . . . . . . . 143.4 Defining the conductance of a nanoparticle array device with the

oxidation state of a molecule . . . . . . . . . . . . . . . . . . . . . . 163.5 Understanding the changes in conductance . . . . . . . . . . . . . . . 203.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

II Non–linear transport through nanoparticle arrays 25

4 Reducing the size of nanoparticle arrays 274.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Fabrication of small nanoparticle arrays . . . . . . . . . . . . . . . . 274.3 Transport measurements at low temperature . . . . . . . . . . . . . . 31

v

vi Contents

5 Characterisation of the nanoparticles in the arrays 355.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Coulomb blockade in a double junction . . . . . . . . . . . . . . . . 365.3 From a double junction to an array of junctions . . . . . . . . . . . . 38

5.3.1 An impedance network model of the nanoparticle array . . . . 395.3.2 Models describing the transport through arrays of nanoparti-

cles linked by tunnel barriers . . . . . . . . . . . . . . . . . . 435.4 Measurements of two dimensional nanoparticle arrays at low temper-

atures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.4.1 Extracting a threshold voltage from the measured data . . . . 455.4.2 Determining the exponent ζ . . . . . . . . . . . . . . . . . . 48

5.5 Broadening of Coulomb blockade induced features . . . . . . . . . . 515.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 The influence of molecules on transport in the nanoparticle arrays 596.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.1.1 A general description of IETS . . . . . . . . . . . . . . . . . 606.1.2 A general IETS measurement of a nanoparticle array device . 62

6.2 Asymmetric transport . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3 Broadening in peaks beyond the threshold voltage . . . . . . . . . . . 676.4 Systematic IETS measurements of nanoparticle arrays . . . . . . . . . 706.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

7 Conclusions and outlook 777.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A Measurements on nanoparticles trapped in nanogaps 89A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

B Measurements on nanoparticles using KPFM 93

C Images of suspended nanoparticle arrays 95

D Protocol for nanoparticle array fabrication 99D.1 Au nanoparticle Synthesis . . . . . . . . . . . . . . . . . . . . . . . 99

D.1.1 Solutions used . . . . . . . . . . . . . . . . . . . . . . . . . 99D.1.2 Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99D.1.3 Extracting gold colloids and covering with a ligand . . . . . . 100D.1.4 Washing the colloids . . . . . . . . . . . . . . . . . . . . . . 101

D.2 Colloid density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102D.3 Preparation of masters for PDMS stamps using UV lithography . . . . 103D.4 PDMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103D.5 Transferring patterns using PDMS stamps . . . . . . . . . . . . . . . 104

Contents vii

D.6 Fabrication of small nanoparticle arrays . . . . . . . . . . . . . . . . 105D.6.1 Substrate cleaning and preparation of PMMA . . . . . . . . . 105D.6.2 E–beam writing and development . . . . . . . . . . . . . . . 105D.6.3 Metal evaporation . . . . . . . . . . . . . . . . . . . . . . . 106D.6.4 SiO2 etching . . . . . . . . . . . . . . . . . . . . . . . . . . 106D.6.5 Cr etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108D.6.6 Stamping of Au nanoparticle arrays . . . . . . . . . . . . . . 108

D.7 Molecular place exchange . . . . . . . . . . . . . . . . . . . . . . . 108

E Electrical characterisation of the dip–stick 109E.1 Frequency response of 10 GΩ resistor in the dip–stick . . . . . . . . . 109

F Taylor expansion of the current measured 113F.1 Details of the Taylor expansion of the current measurements . . . . . 113

G Error calculations 115G.1 Calculation of the broadening in the Coulomb blockade induced

feature due to disorder in the nanoparticle array . . . . . . . . . . . . 115G.2 Calculation of the broadening in the Coulomb blockade induced

feature due to charge disorder in the nanoparticle array . . . . . . . . 116G.3 Calculation of the broadening of peaks beyond the threshold voltage

due to variations in the interparticle separation . . . . . . . . . . . . . 118

H Literature values of phonon modes in molecules 119H.1 Phonon modes in CH3(CH2)8SH and CH3(CH2)7SH molecules on an

Au surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Publication list 121

Curriculum vitae 125

Acknowledgements 127

viii Contents

List of Figures

2.1 A schematic showing the synthesis of Au nanoparticles, the forma-tion of the nanoparticle arrays, and the device preparation. . . . . . . 7

2.2 An overview of nanoparticle array devices used to measure molecularjunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 A schematic of the TTF molecule. . . . . . . . . . . . . . . . . . . . 133.2 The UV–Vis absorption of the TTF molecule in a solution. . . . . . . 143.3 short . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4 The measured sheet conductance of nanoparticle array devices con-

taining the TTFDT molecule and C8. . . . . . . . . . . . . . . . . . . 173.5 Control experiment showing the influence of oxidation and reduction

on devices containing only C8. . . . . . . . . . . . . . . . . . . . . . 183.6 Control experiment showing the influence of oxidation and reduction

on devices containing an OPVDT molecule. . . . . . . . . . . . . . . 193.7 A schematic showing tunnelling processes. . . . . . . . . . . . . . . 223.8 The conductance of devices containing the TTF molecule at different

redox states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1 A schematic showing the structure of the devices with small arrays. . 284.2 A SEM image of the small nanoparticle array devices. . . . . . . . . . 304.3 A schematic of the measurement circuit used to measure small arrays. 32

5.1 A schematic figure of a junction containing a molecular coverednanoparticle between two metal electrodes. . . . . . . . . . . . . . . 36

5.2 An IV curve calculated with the double junction model. . . . . . . . . 385.3 An equivalent circuit of a hexagonal impedance network. . . . . . . . 39

ix

x List of Figures

5.4 A simulation of the voltages in a hexagonal close packed nanoparticlearray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.5 The inverse of the voltage drop per junction in a nanoparticle arrayas a function of array size. . . . . . . . . . . . . . . . . . . . . . . . 42

5.6 An IV curve calculated with the Middleton–Wingreen model. . . . . . 445.7 An IV measurement on a typical device. . . . . . . . . . . . . . . . . 465.8 A dI/dV measurement on a typical device. . . . . . . . . . . . . . . . 475.9 A d2I/dV2 on a typical device. . . . . . . . . . . . . . . . . . . . . . 475.10 IV measurements on seven devices on four samples scaled. . . . . . . 495.11 An IV measurement on a device having several amplitudes of ac

voltage on top of the dc voltage. . . . . . . . . . . . . . . . . . . . . 525.12 An dI/dVmeasurement on a device having several amplitudes of ac

voltage on top of the dc voltage. . . . . . . . . . . . . . . . . . . . . 535.13 An d2I/dV2 measurement on a device having several amplitudes of

ac voltage on top of the dc voltage. . . . . . . . . . . . . . . . . . . . 535.14 The full width at half maximum of the Coulomb blockade peak

measured in a d2I/dV2 curve. . . . . . . . . . . . . . . . . . . . . . . 545.15 An d2I/dV2 measurement on a device at several temperatures. . . . . 555.16 The full width at half maximum of the Coulomb blockade peak

measured in a d2I/dV2 curve. . . . . . . . . . . . . . . . . . . . . . . 56

6.1 A schematic explaining how inelastic tunnelling influences conduc-tance through a metal–molecule–metal junction. . . . . . . . . . . . . 61

6.2 An IV of a typical device. . . . . . . . . . . . . . . . . . . . . . . . . 636.3 A dI/d2 of a typical device. . . . . . . . . . . . . . . . . . . . . . . 636.4 A d2I/dV2 of a typical device. . . . . . . . . . . . . . . . . . . . . . 646.5 A d2I/dV2 of a typical device. . . . . . . . . . . . . . . . . . . . . . 656.6 A schematic showing asymmetric contact between nanoparticle array

and electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.7 A schematic showing the energies associated with asymmetric con-

tact between a nanoparticle and electrodes. . . . . . . . . . . . . . . . 666.8 A schematic showing the energies associated with asymmetric con-

tact between a nanoparticle covered with molecules and electrodes. . . 676.9 A detailed measurement of two peaks beyond the threshold voltage. . 686.10 A fit of Gaussian peaks to peaks in the d2I/dV2 beyond the Coulomb

blockade at several ac voltages. . . . . . . . . . . . . . . . . . . . . . 696.11 The full width half maximum of two IETS peaks. . . . . . . . . . . . 706.12 IETS measurements on a nanoparticle device. . . . . . . . . . . . . . 716.13 IETS measurements on a nanoparticle device. . . . . . . . . . . . . . 736.14 Peak–position probability–density plot of IETS peak positions. . . . . 75

List of Figures xi

A.1 IV measurement of a device containing nanoparticles trapped in ananogap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.2 dI/dV measurement of a device containing nanoparticles trapped ina nanogap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.3 [d2I/dV2 measurement of a device containing nanoparticles trappedin a nanogap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

B.1 AFM and KPFM measurement on a nanoparticle array. . . . . . . . . 94

C.1 An SEM image of a suspended nanoparticle array. . . . . . . . . . . . 95C.2 An SEM image of a suspended nanoparticle array. . . . . . . . . . . . 96C.3 An SEM image of a suspended nanoparticle array. . . . . . . . . . . . 96C.4 An optical image of a suspended nanoparticle array in a TEM grid. . . 97

D.1 A schematic showing details on the angular evaporation used tofabricate the electrodes in the small nanoparticle devices. . . . . . . . 107

E.1 Frequency response of a 10 GΩ resistor in the dip–stick. . . . . . . . 110E.2 IV , dI/dV , and d2I/dV2 measurement of a 10 GΩ resistor in the dip–

stick. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

xii List of Figures

List of Tables

3.1 Comparison of the sheet conductance for devices with differentmolecules during oxidation and reduction. . . . . . . . . . . . . . . . 20

5.1 Fitted and measure values of seven nanoparticle arrays. . . . . . . . . 48

D.1 The RIE etching process. This process will etch ∼200nm of SiO2. . . 107

H.1 A summary of phonon modes in alkanethiols . . . . . . . . . . . . . 120

xiii

Chapter 1Introduction

In recent years electronic devices based on organic molecules have emerged.Recently applications utilising organic light emitting diodes (OLED) have becomeavailable in commercial products. The development of organic, plastic, electronicdevices has paved the way for printable and flexible electronic devices. Modernorganic electronic devices are based on conducting or semiconducting polymers [25].Since polymers are composed of chains of molecules it is reasonable to ask whetherthe function of an electronic device could be derived from a single molecule. Theidea that, indeed, it is possible to construct a functional electronic component out ofa single molecule was put forward in the seventies [5]. As fascinating as the ideamay be, it left a big unanswered question: How does one bring electrical contacts toa single molecule?

Many scientists have pondered the question and many solutions have beenproposed. Most of the devices used to contact molecules today comprise of amolecule bound to a substrate and contacted with an atomically sharp metallictip (STM break junction) or the molecule contacted by a pair of atomically sharpmetallic tips (Mechanically controllable break junction) [46]. These devices workvery well in a laboratory setting, but suffer from the fact that they are not suitedto applications outside the laboratory. Other kinds of devices have also been built,such as self assembled monolayers of molecules on an metallic substrate contactedwith a relatively soft metallic electrode [46]. These devices are prone to metallicshortcuts forming between the electrodes. They are also difficult to use in deviceswhere the function of the device depends on the interaction of the molecules with theenvironment.

Self assembled arrays of metallic nanoparticles can be used as a platform formolecular electronic devices. Devices are then made by coating the nanoparticles

1

2 Introduction

by an organic molecule and allowing the metallic, usually gold, nanoparticles toself assemble into well ordered structures. Devices made from those arrays can beoperated out side of the laboratory and do not depend on specialised equipment toretain their function. The structure of the devices can be such that the moleculescovering the nanoparticles can interact with the environment.

Large arrays, comprising of millions of nanoparticles, are useful as a platformfor molecular electronics. They have been used to measure the conductance ofseveral molecules and even been used to build devices where the function of theindividual molecules, bridging the nanoparticles, defines the function of the device.It is challenging to precisely control the geometry of devices made by arraysof nanoparticles. Making small arrays, where several hundreds or thousands ofnanoparticles make up the array, is difficult. Making these small arrays is usefulif one wants to investigate the details of the transport through the arrays.

In this thesis, we will focus on the challenges stated above. In particular, wewill discuss measurements on nanoparticle array devices, where the function ofthe device is determined by the function of the individual molecules bridging thenanoparticles. We will also see how it is possible to precisely control the geometry ofthe nanoparticle array devices. The ability to make smaller nanoparticle arrays opensup the possibility to investigate the transport through the devices in more detail, aswe will do.

The thesis is presented in two parts. Part I focuses on measurements of activemolecular devices at room temperature. Chapter 2 shows how the nanoparticlearray devices are fabricated. Chapter 3 introduces an experiment where redox–activemolecules were introduced to the nanoparticle array devices and used to tune theirconductance. In Part II we change the temperature and move on towards liquid Hetemperatures. In Chapter 4 we discuss how to fabricate small nanoparticle arrays.We look at the contribution from the nanoparticles to the transport of the nanoparticlearrays in Chapter 5. In Chapter 6 we look at the contribution of the molecules to thetransport in the arrays. In particular, we look at the contribution of the vibrationalmodes of the molecules to the transport. Chapter 7 contains the conclusions and anoutlook on the project.

Part I

Nanoparticle arrays as a platform formolecular devices

3

Chapter 2Device fabrication

2.1 Introduction

The greatest challenge in measuring the electrical properties of a single moleculeis how to contact it with electrodes. To be able to contact a single molecule oneneeds to prepare electrodes that have similar dimensions as the molecule, attach themat the desired positions on the molecule, and hold the assembly stable during themeasurement.

Several methods of bringing electrical contacts to a single molecule have beenused. The most well known methods are the scanning tunnelling microscope breakjunction method [22] and the mechanically controlled break junction [48]. Thesemethods have the advantage of contacting only a single, or a few (< 100) moleculesin parallel, at once. These methods are not practical for device applications since theydo not scale well and due to drift and fluctuations, in these molecular junctions, theyare not stable for more than a few minutes or hours.

One way to contact an individual molecule is to prepare an ordered array ofelectrodes. This array is analogous to the breadboard used for the prototyping ofelectrical circuits. The array provides well defined docking sites where moleculescan interlink the electrodes in the array to produce a network. The network thenconsists of many electrode–molecule–electrode junctions; and each junction is madeup of a single molecule bridging a pair of electrodes.

In order to fabricate an array of electrodes as described above Liao et al.[43] synthesized colloidal Au nanoparticles with a diameter of 10 nm. Thenanoparticles were coated with monothiolated carbon chains (alkane monothiols)to prevent them from aggregating and to control the interparticle distance in thearray. The nanoparticles were then allowed to self–assemble into hexagonally close–

5

6 Device fabrication

packed arrays, where the interparticle distance was ∼2 nm and the curvature of thenanoparticles was such that only a few molecules could bridge two neighbouringnanoparticles. Using nanoparticles with a 10 nm diameter, assuming a ±10% sizedistribution of the nanoparticles, and a 1 nm2 area of the nanoparticle surfaceoccupied by each molecule: Fewer than 100 molecules, each 2 nm long, can bridgetwo neighbouring nanoparticles.

Liao et al. [43] and Bernard et al. [9] demonstrated that the saturated carbonchains coating the nanoparticles can be partially replaced by a new molecule. Bychoosing a molecular rod of the correct length that could bind to gold on each end,Liao et al. [44] showed that a network was formed by the new molecules interlinkingthe nanoparticles. The nanoparticle arrays have been shown to be stable and versatileplatforms for molecular electronics. First of all, the nanoparticle arrays can withstandcommon solvents and thus it is possible to perform molecular place–exchange toinsert new molecules into them [9, 42, 43, 44, 73]. Molecules designed with a specificfunction can retain their function after insertion into the nanoparticle arrays. Thisopens up the way to fabricate functional devices where the function is derived fromthe molecules in the nanoparticle arrays [42, 73].

In this chapter the synthesis of gold nanoparticles, preparation of nanoparticlearrays, and device preparation is described. For full details on the protocol referto Appendix D.

2.2 Preparation of Au nanoparticles and Au nanoparticle arrays

Gold colloidal particles (Au nanoparticles) with a 10 nm diameter were synthe-sized by the reduction of chloroauric acid (HAuCl4·H2O) with trisodium citrate(C6H5O7Na3·2H2O) and tannic acid (C14H10O9) in deionised water (DI-H2O) [43,71], Figure 2.1(a). The nanoparticles were transferred from water to ethanol(CH3CH2OH) by centrifugation and mixed with monothiolated alkane ligands (i.e.C8H18S, hereafter known as C8). The concentration of nanoparticles in the solution is∼ 1013 NP/ml. Typically, 10 ml of a solution containing the nanoparticles in ethanolwas mixed with 200 μl of the ligand. After 48 hours the ligands had covered thenanoparticles. When covered, the nanoparticles precipitated to the bottom of thecontainer. By pipetting the excess ethanol from the container and replacing it withnew ethanol, the excess ligands were removed from the solution. After precipitationthe ethanol was removed and the nanoparticles were dispersed in 4 ml chloroform(CHCl3) by an ultrasonic treatment, Figure 2.1(b).

Patterned 2D nanoparticle arrays were prepared by a combination of self–assemblyand micro–contact printing [43, 61, 62]. The solution of nanoparticles in chloroformwas spread on a convex water surface with a pipette. During the evaporation of thesolvent, the alkanethiol–capped Au nanoparticles self–assembled into a 2D array atthe air–water interface. Patterned polydimethylsiloxane (PDMS, (C2H6OSi)n) stamps


were used to transfer the 2D array from the water surface onto a solid SiO2/Sisubstrate. The pattern consisted of 20 μm wide lines with a spacing of 20 μm[43, 44]. Metallic contact pads (5 nm Ti and 45 nm Au) were evaporated on top of thenanoparticle arrays using transmission electron microscope (TEM) grids as shadowmasks. A device is formed by two adjacent contact pads and the nanoparticle arraybetween them, Figure 2.1(c)–(d). Figure 2.2(a) shows a scanning electron microscope(SEM) image of several devices. The large light squares are the contact pads, the twohorizontal dashed lines emphasise a 20 μm wide nanoparticle array connecting thecontact pads, and the two vertical dashed lines emphasize the length of one device,10 μm, between two contact pads. The array size, within a single device, is ∼ 10 x20 μm2, consisting of ∼107 molecular junctions. Figures 2.2(b) and (c) show SEMimages of a nanoparticle array stamped on a SiO2 substrate. Figure 2.2(b) shows theoverall ordering of the nanoparticles in the array. The array consists of a monolayerof the nanoparticles, globally the nanoparticles form crystallites with a few vacancydefects. Figure 2.2(c) is a close up of the nanoparticle array. It shows that thenanoparticles arrange locally in a hexagonally close packed formation within eachcrystallite. Figure 2.2(d) is a schematic showing how the alkane ligands, white rods,coat the Au nanoparticles, yellow spheres. Dithiolated molecules, blue rods with awhite sphere at each end, can interlink two neighbouring nanoparticles, emphasisedwith a red arrow. The dithiolated molecules can also bind to the nanoparticles withone thiol while the other thiol is free, emphasised with red circles around the whitespheres.

2.3 Au nanoparticle arrays as a platform for molecularelectronics

Arrays of alkane monothiol covered Au nanoparticles can be thought of as a platformfor transport measurements of molecules. After stamping the arrays onto a substrateand depositing electrodes on top of them, a new molecule can be inserted into thearrays. The samples can be placed in a solution containing a relatively high (∼ 1 mM)concentration of the new molecule. Monothiol ligands covering the Au nanoparticlescan be partially replaced by new thiolated molecules[9, 16, 29, 43, 44]. Since thesurface of the nanoparticles is highly mobile there is a probability that an alkanemonothiol is desorbed from it and a new molecule can bind to the nanoparticles wherethere is a vacancy in the alkane layer. If the new molecule is a rod of the correctlength and has groups on both ends that can bind strongly to Au, i.e. thiols, thereis a probability that if it binds to a nanoparticle on one side it may find a vacancyon a neighbouring nanoparticle and bind there. Thus, bridging two neighbouringnanoparticles.

It has been shown that the arrays can resist common solvents such as deionisedwater, ethanol and tetrahydrofouran (THF, C4H8O). Molecular place–exchange in a

2.3. Au nanoparticle arrays as a platform for molecular electronics 9

Figure 2.2: An overview of the devices used to measure molecular junctions. (a) The nanoparticle arraywidth is 20 μm and the distance between two neighbouring contact pads is 10 μm. Each deviceconsists of two large Ti/Au contact pads and the nanoparticle array between them. The scale baris 100 μm. (b) and (c) show close ups of the Au nanoparticle array taken by SEM. Figure (b)shows the global ordering of the nanoparticles in the array. The array is a monolayer, comprisedof crystallites with a few vacancy defects. Figure (c) shows how the nanoparticles arrange in ahexagonally close packed arrangement within each crystallite. Figure (d) is a schematic showingthe relatively large Au nanoparticles covered with octanethiols (white rods) and a conjugatedmolecule of interest (blue double rods). The figure depicts that some of the dithiolated conjugatedmolecules can bridge two neighbouring nanoparticles, highlighted with a red arrow, while othershave only one thiol connected to a nanoparticle and the other thiol is free, highlighted with redcircles around the free thiol.

solvent has been shown to work. Optical and electrical measurements were usedto confirm that dithiolated molecules can interlink neighbouring nanoparticles in thearray. It has been estimated that 20%–40% of the original ligands are replaced bythe new molecules [9, 43, 44]. Figure 2.2(d) illustrates how two Au nanoparticlescovered with monothiols (white rods) can be interconnected by a dithiol (blue doublerod). However, only a fraction of these incoming molecules have a chance to formtwo bonds with the gold surfaces available and effectively bridge two neighbouringnanoparticles. For geometrical reasons, a part of the dithiolated molecules can onlybind to the gold surface via one anchor group, leaving the other end–thiol group freeas shown by spectroscopic characterisation[34].

Chapter 3Adding function to nanoparticle arrays

3.1 Introduction

The field of molecular electronics was started when it was first proposed that onecould build an electrical device which utilised the function of a single molecule placedbetween two electrodes [5]. Since then several groups have pursued this goal andachieved molecular devices which have a function based on the properties of a singlemolecule. Several devices have been fabricated, where the conductance of the devicecan be switched from a high conducting state to a low conducting state and back,due to the properties of a single molecule. The simplest molecule used in such adevice was a single H2 molecule trapped between two gold electrodes of a cryogenicmechanically controllable break junction [70]. There Trouwborst et al. [70] switchedthe conductance of the molecular junction by applying a bias to it. Several otherdevices containing larger organic molecules have also been proposed and fabricated[33].

Using the nanoparticle array platform outlined in Chapter 2 two distinctivelydifferent devices have been produced. The first was an optically sensitive devicebased on a photochromic diarylethene molecule [73]. The conjugation of thismolecule could be altered by exposing it to light at the correct wavelength. Byexposing the molecule in a solution to visible light, in the range from 590 nm to650 nm, the conjugation was broken in the center of the molecule. By exposingthe molecule to UV light, in the range from 300 nm to 400 nm, the conjugationwas restored. This function was preserved when the molecule was inserted into thenanoparticle arrays. Using this scheme the conductance of the nanoparticle arrayscould be switched from a high conducting state, fully conjugated molecule, to a lowconducting state, conjugation broken. This switching was reversible and could be

11

12 Adding function to nanoparticle arrays

repeated several times. These measurements were performed in Ar atmosphere atroom temperature.

In this work, a different scheme involved inserting a Tetrathiafulvalene (TTF,(H2C2S2C)2) molecule into the arrays. TTF is a redox active molecule, meaningthat the charge of the molecule can be changed by oxidation and reduction. The TTFand its derivatives have been used as organic metals and superconductors since theirdiscovery in the 1970’s [8].

In this chapter we discuss how a redox–active molecule, TTF, can be inserted intothe nanoparticle array devices. First we confirm that we can tune the oxidation stateof the molecule in solution, then insert the molecule into the nanoparticle arrays andmeasure the conductance of the devices at different oxidation states of the molecule.To prove that the changes in conductance observed are due to the TTF molecule andnot something else we did two control experiments, which are covered towards theend of the chapter.

3.2 Controlling the oxidation state of a redox–active molecule

The TTF derivative under investigation is depicted in Figure 3.1. The molecule iscomposed of a TTF redox group in the center, three methylene units on each side,and a thiol anchor group at each end of the molecule. From now on the TTF dithiolmolecule will be known as TTFDT.

The oxidation state of the TTFDT can be changed by a chemical reaction usingan oxidant (i.e. iron(III) chloride, FeCl3·6h2O) and a reductant (i.e. ferrocene,Fe(C5H5)2). The absorption spectra of several TTF derivatives, in different oxidationstates, have been measured [75, 76]. The maximum absorption peak of the TTFderivatives has been found to move towards longer wavelengths, towards the red,when the oxidation state changes from the neutral state to the cation–radical (TTF•+)state. Even more redshift is measured when the molecule is oxidised to the dication(TTF2+) state. This redshift of the absorption peak is attributed to an extension of theπ–conjugation of the TTF unit. These measurements indicate that the π–conjugationis especially extended in the case of the dication. The increase in delocalisation ofthe π–conjugation should increase the conductance of the molecule.

Before introducing the TTFDT into the nanoparticle arrays, UV–Vis absorptionmeasurements were used to confirm the reversible redox properties of the moleculein solution. Acetyl–protected TTFDT molecules were used to prevent the reactionbetween two free thiols. The measurements were carried out in a solution ofacetonitrile (ACN, C2H3N). The oxidation to the cation–radical (TTFDT•+) anddication (TTFDT2+) states was performed by respectively adding FeCl3 in an 1:1 anda 2:1 ratio to the TTF in solution. The reduction was performed by adding ferroceneto the solution.

Figure 3.2 shows the UV–Vis absorption of the protected TTFDT in the ACN

3.2. Controlling the oxidation state of a redox–active molecule 13

Figure 3.1: A schematic showing the TTFDT in blue. The molecule is composed of a TTF center, with achain of three methylene units on each side. Terminating the free ends of the methylene chains arethiol groups, which bind to the gold nanoparticles. After oxidation with an superfluous amountof iron chloride two electrons are removed from the TTF center. The molecule can be reducedback to its uncharged state by ferrocene.

solution at different oxidation states. The initial absorption of the molecule is shownwith the blue line. The spectrum has a strong absorption peak around 320 nm anda small shoulder around 370 nm. When the molecule is in the cation–radical state,the black line in Figure 3.2, two absorption peaks are visible one around 450 nmand the second around 700 nm. When the molecule is in the dication state, red line,a single absorption peak is visible around 550 nm. The molecule can be reducedback to the TTF cation–radical state by adding ferrocene to the solution. The greencurve in Figure 3.2 shows the absorption of the TTFDT•+ after reduction and byfurther increasing the amount of ferrocene the molecule is reduced back to the neutralstate shown by the orange curve in the figure. The inset in Figure 3.2 shows theoxidation cycle performed in the measurement and relates the colours of the lines tothe corresponding oxidation states of the molecule.

It is obvious that the absorption spectrum of the TTFDT in the ground state beforeoxidation, blue line in Figure 3.2, and after reduction, orange line in Figure 3.2, is notthe same. This change in the absorption is attributed to the iron chloride and ferrocenein the solution. Figure 3.3 shows the absorption of the TTFDT molecule in ACN, blueline, and the TTFDT in the neutral state after oxidation and reduction, orange line.To verify the contribution of iron chloride and ferrocene to the absorption a solutionwas prepared with the same amount, of iron chloride and ferrocene in ACN, as wasused to oxidise and reduce the TTFDT molecule. No TTFDT molecules were added


Figure 3.2: The absorption of the TTF molecule in a solution of ACN as prepared (blue), oxidised to the+1 state (black), oxidised to the +2 state (red), reduced from +2 to +1 (green), and reducedfrom the +1 to the ground state (orange). The TTF in the ground state shows a single absorptionpeak at 320 nm and a shoulder around 370 nm. The +1 state shows two absorption peaks oneat 450 nm and the other at 700 nm. The +2 state shows one absorption peak at 550 nm. Thedifference between the as prepared TTF and the ground state TTF after reduction can be attributedto oxidised ferrocene in the solution.

to this reference solution. The absorption of the iron chloride and ferrocene in ACNis shown by the green line in Figure 3.3. The curve shows a small peak around 620nm, similar to the peak in the orange curve. This feature stems from the absorption ofoxidised ferrocene in the solution. From these absorption measurements we concludethat the oxidation state of the TTFDT molecule can be controlled by iron chloride andferrocene.

3.3 Introducing function to the nanoparticle arrays

To investigate the influence of the oxidation state of the TTFDT molecule weprepared nanoparticle array devices and inserted the molecule into them. The devicesof nanoparticle arrays were fabricated, as described in Chapter 2, to measure theelectrical properties of the TTFDT. Colloidal Au nanoparticles with 10 nm diameterwere synthesised and coated with octane monothiol ligands. The coated nanoparticleswere allowed to self assemble at a water–air interface and the self assembled arraywas transferred to a Si/SiO2 substrate using patterned PDMS stamps. The pattern on

3.3. Introducing function to the nanoparticle arrays 15

Figure 3.3: The blue line shows the absorption of TTFDT in ACN before oxidation, same as in Figure 3.2.The yellow line show the absorption of the TTFDT in the neutral state after oxidation andreduction, same as in Figure 3.2. The green line shows the absorption of iron chloride andferrocene in ACN with out the TTFDT molecule. The small peak observed around 620 nm canbe attributed to oxidised ferrocene in the solution. The increase in absorption below 400 nm isattributed to the iron chloride in the solution.

the PDMS stamps consisted of 20 μm wide lines. Using a TEM grid as a shadowmask Ti/Au (5 nm/45 nm) contact pads were evaporated on top of the nanoparticlearray.

The conductance of the devices was measured by applying a dc voltage andmeasuring the resulting current through the device. The I–V measurements wereperformed in a probe station in air at room temperature. A National Instrument DAQboard was used to apply the dc voltage. The current was measured by a DL1212I/V converter and the voltage output of the I/V converter was measured by the DAQboard. The measurement was controlled by a LabView program.

After measuring the conductance of the devices with the C8 covered nanoparticlesmolecular place–exchange was used to insert the TTFDT into the arrays. During themolecular place–exchange the TTFDT partially replaces the C8 monothiols coveringthe gold nanoparticles. A solution of 1mM TTFDT in THF was prepared and thesample immersed in it for more than 24 hrs. After molecular place–exchange thesample was removed from the solution, rinsed in THF and blow dried with nitrogengas. TTFDT has eight sulphur atoms. On a bare Au surface any of these eightsulphurs can coordinate with the Au. Since the nanoparticles were covered with


the C8 monothiols during the molecular place–exchange, the TTFDT can only bindto the nanoparticles by the thiol groups at each end of the molecule. Even if theTTFDT could bind to the nanoparticles in a different way, i.e. by other sulphur atomsin the molecule, the distance between the nanoparticles inhibits those molecule frombridging two neighbouring nanoparticles. After the molecular place–exchange theconductance of the same devices as before was measured using the probe stationsetup.

Oxidation was performed by placing the sample in 10 mM iron(III) chloridedissolved in DI–H2O for 40 min, each cycle. After oxidation the sample was removedfrom the solution, rinsed with DI–H2O, and blown dry with nitrogen. After oxidationthe conductance of the same devices was measured again with the probe stationsetup. The oxidised TTF was reduced by placing the sample in a 10 mM solutionof ferrocene in THF overnight. After reduction the sample was removed from thesolution, rinsed with THF, and blown dry with nitrogen gas. After reduction theconductance of the same devices were measured again. These IV measurements wererepeated after each oxidation and reduction step.

The TTFDT in the nanoparticle arrays was only oxidised to the TTFDT+2 state.This is because it is impossible to know exactly how many TTFDT molecules are inthe nanoparticle arrays and thus impossible to add exactly 1:1 ratio of TTFDT:FeCl3.In order to have well controlled experiments we chose to investigate only theTTFDT+2 state. This was easy to obtain by adding a superfluous amount of ironchloride during oxidation.

3.4 Defining the conductance of a nanoparticle array device withthe oxidation state of a molecule

Figure 3.4 shows the sheet conductance G� = G · l/w of 24 devices on one siliconchip obtained from the measured conductance G, where l and w are the distancebetween two electrodes and the width of the nanoparticle array, respectively. Figure3.4(a) shows the sheet conductance of the 24 devices measured while Figure 3.4(b)shows histograms of the conductance values in Figure 3.4(a). The conductancewas measured before molecular place–exchange (turquoise squares), after molecularplace–exchange (dark blue dots), after the first oxidation with excess iron chloride(red up triangles), and the first reduction with excess ferrocene (orange downtriangles).

The conductance is low in the devices containing only C8 in the nanoparticlearrays. This is expected since the C8 molecule is saturated, and thus insulating.Furthermore, these molecules have only one thiol group, binding each molecule toonly one Au nanoparticle. After the molecular place–exchange with TTFDT theconductance of the devices increases by one order of magnitude. This reflects thehigher conductance of the partly conjugated TTFDT molecule. After oxidation in

3.4. Defining the conductance of a nanoparticle array device with the oxidation state of amolecule 17

Figure 3.4: (a) The measured sheet conductance values of TTFDT in Au nanoparticle array devices, 24devices were measured on one sample. The figure shows the conductance of the devices asprepared with C8 (�), after molecular place–exchange with TTFDT (�), after the oxidation(�), and after reduction (�). (b) Histograms of the measurement points in Figure (a). Theconductance increases by an order of magnitude after molecular place–exchange. After oxidationthe conductance increases about a factor of 20. After reduction the conductance is decreased byabout one order of magnitude. The conductance after reduction is about a factor of 2 higher thanthe conductance of the devices after molecular place–exchange and before the oxidation.

an excess of iron chloride the conductance of the devices increases by a factor of20 and after reduction the conductance decreases by one order of magnitude. Theconductance of the devices after reduction is a factor of 2 higher than in the devicesbefore oxidation. This point will be discussed late in this section.

At this point it is tempting to contribute the change in conductance to theoxidation and reduction of the TTF center of the molecules. Indeed the UV–Visspectra of the TTFDT in its neutral and dicationic states clearly differentiate theunderlying molecular obital situations [75]. To prove that the conductance changesare indeed due to the oxidation and reduction of the TTF centers we performed controlexperiments.

Firstly, we wanted to investigate whether ions were getting trapped in the arraysduring oxidation and then removed during reduction. Using a sample with 20devices containing C8 covered Au nanoparticles, we performed the same oxidation–reduction experiment as before. Figure 3.5 shows the sheet conductance of thedevices and a histogram of the measured sheet conductances. The figure shows thatthe conductance of the devices does not change systematically or significantly afterthe oxidation and the reduction. This proves that the conductance of the TTF devices


Figure 3.5: The conductance of 20 devices on one sample, as prepared with C8 (�), after the oxidation (�),and after reduction (�). The figure shows that the oxidation and reduction have no systematic orsignificant effect on the conductance of devices with only C8 covered Au nanoparticles.

was not caused by ions being trapped in the arrays during oxidation and removedduring reduction.

As a second control, we repeated a similar experiment after inserting a conjugatedcompound into the nanoparticle arrays. This compound should not be influencedby the oxidation and reduction agents. Before molecular place–exchange theconductance of 21 as prepared devices, containing only C8, on one sample was mea-sured. After measuring the conductance of the devices dithiolated oligo(phenylenevinylene)(OPVDT) was inserted into the arrays, see inset Figure 3.6 for the molecularstructure. Figure 3.6 shows the sheet conductance of the 21 devices after molecularplace–exchange, blue circles. It is interesting to note in Figure 3.6, that after oxidationthe conductance increases by a factor of 2, red up triangles, and does not decreaseafter reduction, orange down triangles. This is similar to what is seen in Figure 3.4after reduction.

Table 3.1 summarises the results of the three experiments. Gi� corresponds to the

averaged sheet conductance measured after molecular place–exchange, in the case ofthe TTFDT and the OPVDT, or directly after stamping, in the case of the C8. Gox

� andGre� correspond to the average conductances measured after oxidation and reduction,

respectively. In all three experiments we characterised more than 20 devices on asingle silicone chip. The data in Table 3.1 show that devices containing TTFDTcompounds exhibit on average a conductance change of one order of magnitude

3.4. Defining the conductance of a nanoparticle array device with the oxidation state of amolecule 19

Figure 3.6: The measured conductance values of OPVDT in Au nanoparticle array devices, 21 devices weremeasured on one sample. The conductance was measured after molecular place–exchange withOPVDT (�), after the oxidation (�), and reduction (�). After oxidation the conductance of thedevices increases. After reduction the conductance of the OPV does not return to the originalconductance value of the OPV. This is similar to the change observed in devices with TTF, Figure3.4.

while, devices containing C8 the conductance remains constant. Devices containingOPVDT show an increase in conductance of a factor of 2.2 after oxidation while nochange is observed after reduction.

As seen in Table 3.1 the conductance of the devices containing TTFDT or OPVDTmeasured after reduction is not the same as the conductance of these devices beforeoxidation. Rather, the conductance increases by about factor of 2. In the devicescontaining C8 this increase in conductance is not observed. Notice that the C8molecules carry only a single thiol anchor group while both TTFDT and OPVDTcarry two. We attribute the effect described above to the presence of free thiol groupsafter molecular place–exchange. As mentioned in Chapter 2 due to geometricalreasons, only a fraction of the molecules introduced into the arrays during molecularplace–exchange can bind to a gold surface via both thiol groups. This results inthe presence of free unbound thiols in the arrays. It can therefore be expected that,during immersion of the sample in the oxidation solution, the free thiol groups willcoordinate with the iron species present, thereby altering the overall conductance ofthe array. In the case of C8, the situation is different since no free thiols are available.Here, no conductance change was observed after immersion in the oxidation solution.

We have shown that the conductance of the nanoparticle array devices can be


molecule Gi� [nS] Gox

� /Gi� Gre

� /Gi�

TTFDT 0.34 20 ± 4 1.7 ± 0.3C8 0.14 1.0 ± 0.2 1.2 ± 0.6OPVDT 0.65 2.2 ± 0.2 2.3 ± 0.3

Table 3.1: Comparison of the sheet conductance for devices with different molecules during oxidation andreduction. Gi

� corresponds to the averaged sheet conductance measured after molecular place–exchange, in the case of the TTFDT and the OPVDT, or directly after stamping, in the case of theC8. Gox

� and Gre� correspond to the average conductance measured after oxidation and reduction,

respectively. Note that the second and third column indicate a conductance ratio, namely, theconductance after oxidation and reduction normalised with the initial conductance, respectively.

influenced by the oxidation state of the molecules in the array. In the followingsection we introduce two models to help us understand the physics behind the changein conductance.

3.5 Understanding the changes in conductance

To understand the origin of the conductance changes due to the changes in theoxidation state of the TTFDT molecules in the array we look at two models.

In the devices containing the TTFDT molecule an increase of about one orderof magnitude was observed in the conductance after oxidation. To assess thisobserved change in conductance, we first consider a commonly used single–steptunnelling model for the transport through the molecular junction, Figure 3.7(a). Theconductance can be written as:

G = GC exp (−2d√

2Φm/�) (3.1)

Where GC is the contact conductance determined by the coupling to the electrodes,Φ is the barrier height (EHL/2) in units of Joule, d is the length of the molecule,m = 9.1 × 10−31 kg is the electron mass, and � = 1.05 × 10−34 J·s is the reducedPlanck constant. The barrier will be taken as the half of the energy gap between thehighest occupied molecular orbital (HOMO) and the lowest unoccupied molecularorbital (LUMO). This is a crude approximation since we can expect that one of themolecular orbitals, normally the HOMO, will lie closer to the Fermi energy of theAu electrodes than the other. This approximation also assumes that the moleculehas some mean effective barrier while in reality the HOMO–LUMO gap EHL will bedifferent in the TTF center of the molecule than it is in the alkane chains on each side.

Given the presence of the alkane spacers between the TTF center and the –SH binding group we do not expect substantial charge transfer between the Aunanoparticles and the molecule. We therefore anticipate that the molecular orbitalsof the TTF are only weakly affected by the Au terminals. Therefore, we assume that

3.5. Understanding the changes in conductance 21

the Fermi level of the Au terminals lies in the middle of the HOMO–LUMO gap in asymmetric junction at equilibrium. Deviations of the order kBT/EHL can be expecteddepending on the degeneracy of the HOMO and LUMO levels. When the molecule isbrought into the dication state, the molecular orbitals are again filled and the π systemis globally neutral. The situation is therefore analogous to the neutral case, and theFermi level is also expected to lie approximately in the middle of the HOMO–LUMOgap.

The HOMO–LUMO gap of the TTFDT in the dication state was determined fromthe UV–Vis absorption spectrum shown in Figure 3.2. The spectrum shows a strongabsorption peak around 550 nm which reflects a HOMO–LUMO transition. The onsetaround 700 nm gives an estimate of the optical HOMO–LUMO gap. In the neutralcase the optical transition does not correspond to the HOMO–LUMO gap. Therefore,we have to use values from time–dependent density functional theory (TD–DFT)calculations to obtain the HOMO–LUMO gap [3]. Overall, the values obtained forthe HOMO–LUMO gap of the molecule are EHL = 3.7 eV for the neutral TTF andEHL = 1.8 eV for the molecule in the dication state. Using d = 2.2 nm as the lengthof the molecule we calculate the conductance ratio:

GTTFDT+2/GTTFDT = exp⎛⎜⎜⎜⎜⎝−2d

√2m�

·(√Φ+2 − √Φ

)⎞⎟⎟⎟⎟⎠ (3.2)

GTTFDT+2/GTTFDT � 1.1 × 104

Where Φ+2 and Φ are the barrier heights of the TTFDT+2 and TTFDT, respectively.ChemDraw 3D was used to calculate the length of the molecule by minimisingits energy using the MM2 force field and measuring the distance between the twoterminal sulphur atoms.

The estimate of the conductance change given by this simple tunnelling model isalmost three orders of magnitude larger than the measured change (� 20). There areseveral reasons why this might happen. An obvious reason for the discrepancy is theapproximation of the effective tunnelling barrier height is simplistic. Furthermore,it does not take into account any possible charging effect and reorganisation of themolecular orbitals upon contacting the Au electrodes. The estimate given by thismodel can be looked at as an upper limit of the conductance change after oxidationof the TTFDT.

A two step tunnelling model would be more appropriate to describe the process inthis system. In fact, the alkane linkers were added to the TTF center to reduce thecoupling between the TTF and the electrodes. A HOMO–LUMO gap of about 7 eVcan be expected for short alkane chains [60]. This decoupling is essential to ensurestable oxidation and reduction of the molecule. Such a configuration suggest that aresonant tunnelling model is more appropriate to describe the process, Figure 3.7(b).

The TTF center plays the role of a weakly coupled quantum dot and thealkane chains act as large barriers. At low bias voltages, the conductance can be


Figure 3.7: A schematic showing two tunnelling processes. (a) A simple one step tunnelling process wherean electron tunnels from the left to the right electrodes. The molecule, between the electrodes,is treated as a tunnelling barrier. Here Φ is the barrier height and d the distance between theelectrodes. (b) A two step tunnelling process. An electron tunnels from the left electrode througha large barrier onto the molecule and then again through a large barrier onto the right electrode.The tunnelling rates through the barriers are indicated by Γ1 and Γ2, and ε is the energy differencefrom the closes molecular orbital and the Fermi level of the electrodes.

approximated by:

G =2e2

hΓ1Γ2

ε2 + (Γ1 + Γ2)2/4(3.3)

Where Γ1 and Γ2 are the electronic coupling between the molecule and the left andright electrodes, respectively, ε is the energy difference between the closest molecularorbital and the Fermi level of the reservoirs, e is the charge of an electron, and h thePlanck constant. Since the molecule is symmetric we assume Γ1 = Γ2 = Γ. In theweak coupling limit Γ << ε. The weak coupling approximation can be justified bythe presence of the alkane linkers. In a similar study on an asymmetric C60–basedsystem with a slightly different but comparable linker, the authors found a couplingconstant Γ � 5 meV[23]. The change in conductance can be expressed as:

GTTFDT+2/GTTFDT =

(εTTFDT

εTTFDT+2

)2

(3.4)

GTTFDT+2/GTTFDT � 4.2

This second estimate is about a factor of 5 lower than the observed change inconductance. This model is an oversimplification since the distance between theFermi energy and the closest orbital relevant for transport might not by simply afraction of EHL. This model does not take into account any charging effects or energylevel broadening. While phenomenological, the above estimates remain reasonableand provide an upper and a lower bound to the conductance ratio expected in themeasurement.

To examine the reversibility of the conductance change upon exposure to the

3.5. Understanding the changes in conductance 23

Figure 3.8: The device conductance normalised with the conductance of the devices before TTF molecularplace–exchange averaged over the 20 devices measured as a function of redox step, TTF (�),after oxidation (�), and after reduction (�). The switching amplitude decays with the number ofrepetitions. This might be caused by the breaking of Au–S bonds between the TTFDT and thenanoparticles by the oxidant and the coordination of the unbound end groups with iron ions fromthe oxidant. There is also a possibility of the formation of dimers and oligomers via disulphidebond formation during the redox cycles.

oxidant and reductant, we repeated the redox process several times. Figure 3.8shows the average ratio G� TT FDT /G� C8 of 24 devices at different stages during fouroxidation–reduction cycles. The red points correspond to the oxidised, dication, statewhile the orange pints correspond to the neutral state. The data demonstrates that theconductance of the devices can be reproducibly switched between a high conductancelevel, after oxidation, and a low conductance level, after reduction. Note that theswitching amplitude decays with the number of repetitions. This might be causedby the breaking of Au–S bonds between the TTFDT molecule and the nanoparticlesby the oxidant and the coordination of the unbound end groups with iron ions of theoxidant. We also cannot exclude the formation of dimers or oligomers via disulphidebond formation during the redox cycles. Such effects will result in a lower maximumconductance and a higher minimum conductance.


3.6 Summary

We have successfully inserted molecules with tetrathiafulvalene redox units into two–dimensional nanoparticle arrays to form functional networks of molecular junctions.The conductance of the networks could be repeatedly switched between a highconductance level and a low conductance level by means of chemical oxidation andreduction. The change in conductance arises from the reorganisation of the TTFDTmolecular orbitals upon oxidation, as supported by UV–Vis spectroscopy. The high–and low–conductance states are stable enough to permit electrical characterisationafter each oxidation and reduction step. Our experiments not only demonstrate theefficient modulation of the conductance of molecular junctions by up to one orderof magnitude but also raise interesting prospectives for chemical sensing based onnetworks of active molecular junctions.

Part II

Non–linear transport through nanoparticlearrays

25

Chapter 4Reducing the size of nanoparticle arrays

4.1 Introduction

In Part I we introduced the nanoparticle arrays as a platform for molecular electronics.One could think of them like the breadboards used to design and test electroniccircuits. Instead of resistors and capacitors inserted into the breadboard, moleculescan be inserted into the arrays to bridge the nanoparticles. Furthermore, we discussedhow the conductance of the arrays was influenced not only by the molecules used tobridge the nanoparticles, but also the oxidation state of those molecules.

The bias voltages applied to the arrays in Part I were on the order of ± 10 V.Assuming that the applied voltage drops evenly over each molecular junction inseries, the voltage drop over each molecular junction is only on the order of 10 mV.The devices described in Section 2.3 are relatively large, ∼ 10 × 20 μm2 in sizecontaining ∼ 1000 × 2000 molecular junctions in series and parallel. To investigatethe transport through the nanoparticle arrays in more detail, it is necessary to fabricatesmaller arrays. Using PDMS stamps to make small structures is not feasible, PDMSis not rigid enough to support narrow high aspect ratio structures. Using the proceduredescribed in Section 2.3, it is impossible to bring the metal electrodes closer to eachother than a few micrometers. Therefore, a new method had to be devised to fabricatenanoparticle arrays with dimensions on the order of hundreds of nanometers.

4.2 Fabrication of small nanoparticle arrays

To make the small nanoparticle arrays Ti/Au electrodes were evaporated on top ofa Si/SiO2 substrate. The SiO2 had a thickness of 400 nm, and the electrodes were

27

28 Reducing the size of nanoparticle arrays

Figure 4.1: A schematic showing the structure of devices with small nanoparticle arrays. (a) A top and a sideview of the structure of the device on top of 400 nm thick SiO2 after the two evaporation steps.The device structure is determined by the Cr etching mask. In the first evaporation step the Ti,Au, and the Cr on top of the Au are evaporated. The Ti and Au layers are evaporated at ± 7◦ and0◦ angles from the normal of the substrate. The Cr layers are evaporated at ± 8◦ and 0◦ anglesfrom the normal. This results in the thickness of the electrodes decreasing towards the center ofthe device. The Cr layer on the SiO2 is evaporated in the second evaporation step at 0◦ angle fromthe normal of the substrate. This Cr layer defines the size of the nanoparticle array measured inthe device. (b) The device after the SiO2 and the Cr have been etched away. (c) A top and a sideview of the device after stamping with the nanoparticle array. The array is deposited everywhere,but the 400 nm height difference between the device and the surrounding substrate ensures thatthe array on top of the device is not connected to the surrounding substrate. The height decreasein the electrodes, near the center of the device, ensures the continuity of the nanoparticle arrayover the whole device.

24 nm thick structured in a way to become gradually thinner towards the ends. Thestructure is shown in Figure 4.1 and described in details below. The electrodes werepatterned using electron beam lithography, metal evaporation and etching.

First the electrode pattern was written into a PMMA–MA/PMMA layer with athickness of 100 nm and 600 nm, respectively. The PMMA–MA layer provides alarge undercut under the PMMA layer. Titanium (Ti) and gold (Au) layers wereevaporated at three different angles, thus creating gradually decreasing electrodethickness towards the center of the device. The electrode metals were evaporated at ±7◦, and 0◦ angles from the normal of the substrate. The thickness of each Ti layer ateach angle was 3 nm, and the thickness of the three Au layers was 5 nm at each angle.This results in 8 nm high steps. After evaporating the Ti and the Au layers three 15 nmthick chromium (Cr) layers were evaporated on top of the Au at ± 8◦, and 0◦ anglesfrom the normal of the substrate. After lift off PMMA–MA and PMMA were again

4.2. Fabrication of small nanoparticle arrays 29

spun on the substrate and a second lithography step was performed. In the secondlithography step lines were patterned on the substrate connecting the two electrodes.After development a 45 nm thick Cr layer was evaporated onto the substrate at a0◦ angle from the substrate normal. This Cr layer covered the SiO2 between the twoelectrodes.

After lift off the substrate was treated with O2 and CHF3 plasma to etch awaythe uncovered SiO2. Then the Cr was etched away with a solution of cericammonium nitrate (CAN, Ce(NH4)2(NO3)6) in DI-H2O and acetic acid (CH3CO2H).The resulting structure comprised of the electrodes on top of 400 nm thick SiO2

bridged by a small SiO2 area. The electrodes having a thickness of 9 nm Ti and 15nm Au became gradually thinner, in steps of 8 nm, close to the SiO2 bridge. The sizeof the SiO2 bridge determined the size of the nanoparticle array in the device.

After fabrication of the electrodes the samples were soldered to a chip carrierusing flux free solder. This provided the possibility of performing molecular place–exchange on the samples in organic solvents without having unwanted organicmolecules influencing the exchange.

Using un–patterned PDMS stamps Au nanoparticle arrays were stamped on topof the substrate. The 400 nm height difference between the electrodes and thesurrounding Si substrate caused the nanopartice array on the electrodes to be disjointfrom the surrounding nanoparticle array while the 8 nm step towards the SiO2 bridgeallowed the array to be continuous over the whole device, the two electrodes and theSiO2 bridge between them. The result were well defined nanoparticle arrays with alength of 200–500 nm and width of 200–1000 nm contacted by two metal electrodes.

After stamping the electrodes were connected to the contacts of the chip carrierusing Au wire wedge bonding. The substrate was also connected to a contact padon the chip carrier using Al wire wedge bonding. This allowed the substrate tobe grounded during measurements, thus reducing the effect of leakage through thesubstrate between the electrodes.

Figure 4.2 shows images of an actual sample. Figure 4.2 (a) is an optical imageof a sample in a chip carrier after stamping with a nanoparticle array and bonding.The chip carrier is 1 cm2. The sample is fixed into the chip carrier by soldering. Thesolder used contains no flux, thus no organic material. This is important to reducethe probability of foreign organic molecules disturbing molecular place–exchange.Figure 4.2 (b) is a SEM image of the sample, showing the device contact padssurrounding the devices, which reside in the center. Figures 4.2 (c) shows a closerlook of three devices in the center. The leads come in from left and right to eachdevice. A nanoparticle array has been stamped on top of the sample in the figure. Thefigures is taken at a 70◦angle from the normal to the substrate. It shows the raisedstructure of the electrodes and how the nanoparticle arrays on top of the electrodesare not connected to the nanoparticle arrays deposited on the Si substrate aroundthe leads. Figure 4.2 (d) shows a close up of a device before the deposition of thenanoparticle array. The two Au electrodes, yellow, are separated by a SiO2 bridge


Figure 4.2: (a) A photo of a bonded sample in a chip carrier taken by an optical microscope. The sample issoldered in the chip carrier to mechanically fix it. The contacts of the devices are bonded with anAu wire to the contacts of the chip carrier. (b) An SEM image of the sample. The scale bar is100 μm. (c) A closer look at the devices taken by an SEM at 70◦ angle from the normal of thesurface. The image shows the raised structure of the electrodes. The scale bar is 2 μm. (d) Aclose up of a device before the nanoparticle array was stamped on it. The yellow areas representthe Au electrodes. The light blue area in the center is the SiO2 where the nanoparticle array willwe deposited later. On each side of the SiO2 one can see the steps in the Au electrodes. Thedark areas above and below the SiO2 in the figure are the exposed Si substrate. The scale bar is200 nm. (e) A close up of a device, after the nanoparticle array has been stamped on it, taken byan SEM. The figure shows that the nanoparticle array is continuous over the whole device. Thecolours are the same as in Figure (d) and were added by Adobe Photoshop CS. The scale bar is200 nm.

4.3. Transport measurements at low temperature 31

shown in a light blue color in the center of the image. The dark areas above andbelow the SiO2 bridge are the Si substrate. Towards the SiO2 bridge one can see thesteps in the Au electrodes. Figure 4.2 (e) shows a device after the deposition of thenanoparticle array. The figure shows clearly that the nanoparticle array is continuousover the device. Furthermore, it shows that no nanoparticles are deposited on the Sisubstrate next to the device. In Figures 4.2 (d)–(e) the color was added using AdobePhotoshop CS.

4.3 Transport measurements at low temperature

The transport properties of the devices were measured using the set up shown inFigure 4.3. The sample, already placed in a ceramic chip carrier, was inserted intoa socket at the end of a dipstick. The socket of the dipstick was wired to a breakout box, on top of the dipstick, with a ribbon of 12 twisted pair wires. The sampledevices were connected in such a way that one wire in a twisted pair was connectedto one side of the device and one wire in another twisted pair was connected to theother side of the devices. Normally wires from the first twisted pair were used withwires from the seventh twisted pair, wires from the second with wires from the eighthand so on. While measuring, all wires of all the twisted pairs are grounded, exceptfor the two wires needed for the measurement. This spatial separation of the wiresused, and the grounding of all other wires decreased the capacitive cross talk betweenthe measurement lines.

The dipstick was characterised by measuring a 10 GΩ resistor that was soldered toa chip carrier and inserted into it. The measurements were done at room temperature.The differential conductance of the resistor in the dipstick was measured while thefrequency of the applied ac voltage was varied from 11 Hz to 11 kHz, the dc bias wasat 0 V during the measurement. From the frequency sweep we calculated the leakagecapacitance to ground in the dipstick to be ∼ 2 pF. The IV , dI/dV , and d2I/dV2 werealso measured using the 10 GΩ resistor. The frequency of the ac voltage was 73 Hz.The measurement data are to be found in Appendix E.

The measurements were controlled with a LabView program on a PC. The programwas used to control a Yokogawa YK7651 dc voltage source and two StanfordResearch SR830 lock–in amplifiers, one set to detect the first harmonic of the acsignal and the other to detect the second harmonic of the signal. The resulting currentwas detected using a DL Instruments DL1212 IV converter. The dc part of the signalwas measured on a National Instruments data acquisition board (NI–DAQ). The acpart of the signal was measured by the two lock–in amplifiers and their output passedon to the data acquisition board and the PC.

When performing the measurement a small ac voltage signal was added on topof a dc voltage signal via a NLT1 1:1 transformer. The dc voltage is supplied bythe Yokogawa voltage source. The ac voltage was supplied by one of the lock–in

4.3. Transport measurements at low temperature 33

amplifiers. The large ac signal was passed through a voltage divider to decrease thedigitisation error in the signal. The lock–in amplifiers were synchronised using theTTL signal from the amplifier set to detect the second harmonic of the ac signal. Thislock–in amplifier also supplied the ac signal.

The capacitance between the device electrodes and the substrate is C = Aε0εr/d withA ∼ 150 × 150 μm2, d = 400 nm, ε0 is the permittivity of vacuum, and εr = 3.9 forSiO2. The capacitance is C = 1.9 × 10−12 F. The substrate was grounded throughan 1 μF capacitor. This capacitor is about six orders of magnitude larger than thecapacitance between the device electrodes and the substrate. An ac signal is thuseffectively grounded while any dc charging in the substrate is not grounded. Thisreduces the dc voltage drop from a device contact to the substrate over the oxide andthus reduces the probability of the oxide breaking down under high dc bias.

The current flowing in the device is comprised of an ac part and a dc part and canbe expressed by a Taylor series as

I(Vdc + Vac sin(ωt)) = I(Vdc)dI(Vdc)

dVVac sin(ωt) +

+14

d2I(Vdc)dV2 V2

ac cos(2ωt + π) (4.1)

For details on the calculation see Appendix F.

Chapter 5Characterisation of the nanoparticles in thearrays

5.1 Introduction

The transport through arrays of nanoparticles is governed by several competingenergy scales. Regarding the nanoparticles, their charging energy and the tunnellingconductance between them are important [7]. These energy scales can be adjustedby tuning the size of the nanoparticles, the interparticle spacing and the interparticlecoupling. The interparticle spacing and coupling can be adjusted by the moleculessurrounding the nanoparticles. Having perfect control over these parameters wouldopen up a large range of possible devices where the device function would bedetermined by the properties of the nanoparticle arrays. Metallic nanoparticles can beviewed as artificial atoms and therefore arrays of nanoparticles could be engineeredinto artificial solids with tunable electronic and optical properties [7].

The nanoparticles form the basis of the nanoparticle array, therefore it is importantto understand their contribution to the transport in the arrays. The transport througharrays of metallic nanoparticles has been studied experimentally [78]. The questionswe strive to answer concern the detailed transport through the molecules bridging thenanoparticles. Understanding the contribution of the nanoparticles in the transport isthe first step towards understanding the transport through the molecules in the array.

In this chapter, we investigate what the contribution of the nanoparticles to thetransport in the arrays is and what role disorder of the arrays plays in the transport.

35

36 Characterisation of the nanoparticles in the arrays

Figure 5.1: The generic model of transport through two tunnel junctions connected in series. The model iscomprised of a nanoparticle contacted to two electrodes via an RC circuit. Figure (a) shows a RCmodel of the tunnel junctions. The nanoparticle is coupled to the two electrodes via capacitors Cjand resistors Rj , where j is the junction number. The tunnelling rates onto and of the nanoparticleare indicated by Γ+j , and Γ−j , respectively. Electrode 1 is at bias Vb and Electrode 2 is at ground.Figure (b) shows the energy scales relevant to transport through the junction. The change inenergy when a single charge is added (+) or removed (-) is indicated by ΔU±. The total potentialdifference between the electrodes is Vb.

5.2 Coulomb blockade in a double junction

The nanoparticles forming the arrays are quite small. They have a radius of 5 nmand are small enough so that a charge moving onto or off the nanoparticle willfeel the force of the charges which are already on it. This gives rise to a voltagedependent impedance in the array. This phenomenon is the single–electron chargingof the nanoparticle. When an electron tunnels onto or off the nanoparticle its chargechanges. The energy required to charge the nanoparticle must be supplied from theenvironment, either thermally or from the external applied bias. This is known asCoulomb blockade and gives rise to the nanoparticle charging energy [78].

A simple model has been set forward to describe the transport through a nanoparti-cle in the single–electron charging regime [2, 24]. The model describes the transportthrough a series of two tunnel junctions. A schematic of the system is shown inFigure 5.1. We start by introducing this model and later build on it when the transportthrough an array of nanoparticles is characterised.

The transport through the model system will be governed by the energy needed toadd or remove charge to/from the nanoparticle. This charging energy of the metallicnanoparticle is calculated as [40]

Ec =e2

2C, (5.1)

where e is the elemental charge of an electron and C the capacitance of the

5.2. Coulomb blockade in a double junction 37

nanoparticle. The capacitance of a single spherical nanoparticle is

C = 4πε0εrR, (5.2)

where ε0 is the permittivity of free space, εr the dielectric constant, and R the particleradius. The change in charging energy of the nanoparticle when a single charge isadded (+) or removed (-) is calculated as

ΔU± =(Q ± e)2

2CΣ− Q2

2CΣ, (5.3)

where CΣ = C1 + C2 is the sum of the capacitances in Figure 5.1 and Q is the chargeon the nanoparticle. The change in the energy of the system when an electron tunnelson or off the nanoparticle is

ΔE±1 = ΔU± ∓ eC2

CΣVb,

ΔE±2 = ΔU± ± eC1

CΣVb, (5.4)

where Vb is the potential difference between the two electrodes. The first term in theequation is the change in the electrostatic energy of the nanopartice ΔU± as defined inEquation 5.3. The second term in the equation is the work done by the voltage sourcewhile the electron tunnels over the junction j. The voltage drop over each junction inFigure 5.1 is

Vj =C1C2

C jCΣVb. (5.5)

The tunnelling rate is controlled by the resistors in Figure 5.1

Γ±j =1

e2Rj

−ΔE±j

1 − exp(ΔE±j /kBT

) . (5.6)

At T = 0 K, Equation 5.6 can be simplified as

Γ±j (T = 0K) ={ −ΔE±j /e

2Rj, ΔE±j < 0,0, ΔE±j ≥ 0, (5.7)

assuming a symmetric junction with R1 = R2, C1 = C2, and with no initial chargeon the nanoparticle Q = 0. Combining Equations 5.1, 5.3, 5.4, and 5.7 the thresholdvoltage for conductance in the presence of Coulomb blockade in a symmetric doublejunction is found to be

|VCB| = 2EC/e. (5.8)


The current through the double junction is determined by the difference in thetunnelling rates on to and off the nanoparticle

I = e(Γ+1 − Γ−1

)= −e

(Γ+2 − Γ−2

). (5.9)

Combining equations 5.7 and 5.9 the current flowing through the double junction is

−1 −0.5 0 0.5 1−0.5

0

0.5

I[A

]

Vb [V]

−|VCB|

|VCB|

Figure 5.2: The IV curve calculated byEquation 5.10 with |VCB | = 0.5and R = 1 Ω.

I =

⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

Vb − |VCB|2R

Vb > |VCB|,0 −|VCB| < Vb < |VCB|,

Vb + |VCB|2R

Vb < −|VCB|.(5.10)

5.3 From a double junction to an array of junctions

The double junction model introduced in Section 5.2 captures the dynamics oftransport through a single nanoparticle between two electrodes. The devices wemeasure contain many nanoparticles, in series and parallel, between two electrodes.The problem we face is how to understand the role of Coulomb blockade in sucharrays. One way to use the model in Section 5.2 to model the junctions in the arrays isto see if we can treat the array as a simple parallel and series connection of junctions.Can we estimate the voltage drop over each junction by dividing the total voltageby the number of junctions in series and can we estimate the current through eachjunction by dividing the total current measured by the junctions in parallel? Mappingthis in details would be an interesting measurement requiring high resolution Kelvinprobe force microscopy (KPFM). This is beyond the scope of this work. Although,in a collaboration with Thilo Glatzel and Marcin Kisiel, in the group of Ernst Meyerat Basel University, we have started looking at the arrays with a KPFM. An overviewof preliminary measurements is in Appendix B. To gain some insight into the voltagedrops over the junctions in the arrays we have made simple models using linear circuitelements.

5.3. From a double junction to an array of junctions 39

Figure 5.3: Schematics of hexagonal impedance networks. Metallic electrodes (yellow circles) are connectedvia an impedance Z. A voltage Vb is applied to the topmost electrode while the bottommostelectrode is kept at ground potential. The proportional voltage at each electrode is indicatedin each yellow circle. The currents flowing in the circuit are shown with color coded arrows.Each color represents the magnitude of the current, currents with the same color have the samemagnitude. Here two cases are shown: (a) The side–to–side case when two electrodes areconnected to the bias source and another two to the ground. The voltages at each electrodecan be readily obtained. The same current flows through each impedance going from top tobottom and thus the same voltage drops over each of them. There is no voltage drop over theimpedances going from left to right and no current flows there.(b) The head–to–tail case whenonly one electrode is connected to the bias source and another electrode to the ground. The head–to–tail case is comprised of the same hexagonal unit as the side–to–side case, but rotated by 30◦.The head–to–tail case is more complex to solve, than the side–to–side case, and the voltages ateach electrode cannot practically be calculated analytically for large arrays.

5.3.1 An impedance network model of the nanoparticle array

In a first attempt to investigate how voltages drop and how currents flow in the arraywe start by looking at what happens in a single hexagonal unit comprising of acentral nanoparticle surrounded by six nanoparticles. Figure 5.3 shows a schematicof an electrical circuit where metal electrodes, yellow circles, are connected withimpedances Z. A potential Vb is applied to the top electrode while the bottomelectrode is kept at ground potential. The voltage at each nanoparticle is indicatedinside it, as a fraction of the applied voltage. The figure shows two cases: The side–to–side case, has two electrodes connected to the voltage source and two connected tothe ground and the head–to–tail case, where only a single nanoparticle is connectedto the voltage source and a single nanoparticle is connected to the ground. The twocases consist of the same hexagonal unit, but rotated by 30◦.

Due to symmetry in the side–to–side case the same voltage drops over eachimpedance going from top to bottom, while no voltage drops over the impedancesgoing from left to right. Thus, the voltage drop over each impedance scales as the


number of lines of nanoparticles, Vjnct = Vb/(N−1), where N is the number of lines ofnanoparticles. This can be related to the voltage drop over each molecular junction inthe nanoparticle array assuming each molecular junction has an impedance Z. In thecase when the measured array is monocrystalline with the side–to–side orientationthe voltage drop per molecular junction scales as

Vjnct =

√3

2Vb · dL − h

, (5.11)

where L = h(N − 1) is the distance between the electrodes connected to the array, dis the distance from center to center of the nanoparticles, h = d

√3/2, and Vb is the

voltage applied to the electrodes connected to the array.

The current in the array scales with the array width. The arrays are assumed to bea monolayer so the thickness is not a factor. The linear current density in the array isdefined as the current flowing in each current path. In the side–to–side configurationthe current scales with the number of vertical columns as

Idens =12

ItotaldW − d

, (5.12)

where W = d(M−1)/2 is the width of the array, d is distance from center to center ofthe nanoparticles, M is the number of columns, and Itotal is the total current flowingin the array.

In the head–to–tail case the voltage drop over each impedance is not alwaysidentical. Solving for the voltages at each nanoparticle analytically is not practical forlarge arrays. To investigate the influence of scaling the array we used PSpice Studentversion Release 9 by OrCAD to calculate the voltages of nodes, representing thenanoparticles, connected by identical resistors in the head–to–tail formation. Figure5.4 shows the results of the simulation for: (a) The basic hexagonal unit, sevennanoparticles the center one connected to the outer six; (b) A narrow array withthree hexagonal units in series; (c) An array with two hexagonal units in series anda two hexagonal in parallel; (d) The generic array. The color of the nanoparticles,circles, indicates their potential. Red indicates that the nanoparticle is at the highestpotential, equal to Vb, and white indicates that the node is at ground potential, shadesin between red and white indicate intermediate potentials. The lines connecting thecircles represent the potential difference between two neighbouring nanoparticles,the voltage drop over a resistor in this model. The blue color indicates the highestvoltage drop over a resistor in the model array and white indicates no voltage dropover the resistor. The most prominent lines in the figure imply the highest voltagedrop between the nanoparticles. The blue color bar indicates the fraction of theapplied bias voltage that drops over the resistor. Looking at the scale by the bluecolor bar one can see how the maximum voltage drop decreases when the units areconnected in series. Connecting the units in parallel does not change the voltage drop


Figure 5.4: A Spice simulation of metallic electrodes connected by identical resistors. The electrodes arearranged as the nanoparticles in the nanoparticle array in the head–to–tail case. (a) The smallestunit containing a full hexagon. (b) Three hexagonal units in series. (c) Two hexagonal units inseries and two in parallel. (d) A representation of the generic array. The color of the circlesindicates their voltage with red representing 100% of the applied voltage and white the groundpotential. The color of the lines connecting the circles indicates the voltage drop over eachresistor. Here the blue color indicates the largest voltage drop over the resistor. The fraction ofthe applied voltage dropping over each resistor is indicated on the blue color bar. The voltageper junction decreases as the number of electrodes in series increases. The rate of the decreaseis shown in Figure 5.5. The voltage drop per junction does not change significantly as morejunctions are added in parallel.

over the resistors. Figure 5.5 shows how the inverse of the voltage drop over eachresistor scales with the number of lines of nanoparticles in the array. The red circlesare values calculated using Equation 5.11, and the blue circles were obtained fromthe Spice simulations. The dotted lines are guides for the eye. The insets in the figureshow the orientation of the hexagonal unit with red showing the side–to–side caseand blue showing the head–to–tail case, as well as the slope of the lines.

As shown in Eq. 5.11 the voltage over each junction in the side–to–side casedecreases as 1/(N − 1). In the head–to–tail case the voltage over each junctiondecreases as 3/N, so the voltage drop over each junction as a function of the distance


Figure 5.5: The inverse of the voltage drop per junction in the nanoparticle array as a function of the numberof lines in the array. In the side–to–side case, red circles, the voltage drop per junction decreaseslinearly with the increase in the number of lines. The values plotted in the figure are calculatedusing Equation 5.11. In the head–to–tail configuration, blue circles, the voltage drop per junctiondecreases with the increasing number of lines in the array with a factor of 3. The data plotted inthe figure was obtained by the Spice simulation.

between the electrodes is then

Vjnct =32

Vtotal · dL − d

, (5.13)

where L = d(N − 1)/2.The number of current paths scales as the number of vertical columns of

nanoparticles. The current density can be estimated as

Idens =

√3

2ItotaldW − h

, (5.14)

where W = h(M − 1) is the width of the array, h is as defined in Eq. 5.11, and Itotal isthe total current flowing in the array.

In reality the nanoparticle array bridging two electrodes is neither perfectly inthe head–to–tail nor the side–to–side configuration. Moreover, the array has somevariations in the impedance of each molecular junction due to the size distribution ofthe nanoparticles and defects in the array. The array is also never monocrystallinebetween the electrodes and the effect of grain boundaries on the transport of thearray is not known. In this thesis we assume L � d, h and normalise the appliedvoltage by d/L to obtain the voltage drop over each junction. Furthermore, Middleton


and Wingreen [47] showed that, in a two dimensional array of capacitively couplednormal–metal dots arranged in a square lattice, the onset of conduction occurs at avoltage Vth proportional to the linear array size. Tran et al. [67] report that the biasper junction and the bias applied across a short stack of N particles is Vjnct = Vtotal/N.

As with the voltage scaling the linear current density will not scale exactly asdescribed in Equations 5.12 and 5.14. From now on the total current will be scaledby d/W to find the linear current density, assuming W � d, h. As a consequence ofthis, scaling, the sheet conductance of the devices is found by scaling the measuredconductance by L/W, and the second derivative of the current–voltage response isscaled by L2/W to remove the influence of the array geometry from the signal.

5.3.2 Models describing the transport through arrays of nanoparticleslinked by tunnel barriers

Modelling the nanoparticle array as nodes connected by resistors is useful to learnhow to calculate the voltage drop over, and the current through, a single junction.This model does not take into account the properties of the nanoparticles introducedin the tunnelling model in Section 5.2. The transport through an array of nanoparticlescoupled via tunnelling junctions has been studied by several groups. Here we lookmore into the details of those models.

The first thing to consider is how the charging energy of a nanoparticle changeswhen the particle is placed in an array of many nanoparticles which can interactwith each other. The charging energy of the nanoparticle in the array depends onthe inter–nanoparticle coupling, since a charge on one nanoparticle can polarize itsneighbouring nanoparticles. The capacitance of the nanoparticles in the array canbe approximated by assuming that the nanoparticle is separated from a conductingcontinuum by an insulating shell. The nanoparticle capacitance can then be calculatedas [78]

C = 4πε0εrR(R + s)

s(5.15)

where s is the interparticle separation. This in turn affects the charging energy Ec

calculated in Equation 5.1 and thus the threshold to over come Coulomb blockadecalculated in Equation 5.8.

The effective capacitance of the nanoparticles is not enough to model a wholearray. Effects of random charges on the nanoparticles and meandering current pathsin two dimensions need to be considered. Elaborating on the double junction modelMiddleton and Wingreen [47] describe the collective transport in arrays of smallmetallic dots. They define their array as capacitively coupled, via tunnel junctions,metallic dots in one or two dimensions. The onset of conduction is found to occur ata voltage Vth proportional to the linear array size. The current at voltages above Vth

in linear and square arrays is found to behave as


−1 −0.5 0 0.5 1−1

−0.5

0

0.5

1

Vb [V]

I[A

]

−|Vth|

|Vth|

Figure 5.6: The IV curve calculated by Equation5.16 with |Vt | = 0.5 and ζ = 5/3.

I ∼ (Vb/Vth − 1)ζ (5.16)

Figure 5.6 shows the shape of the cur-rent calculated by Equation 5.16 usingthe parameters Vth = 0.5 and ζ = 5/3.There are two characteristic parameters inthe model namely the threshold voltageVth and the exponent ζ. We will nowdiscuss the two parameters, starting withthe threshold voltage.

The threshold voltage in Equation 5.16is closely related to |VCB| in equation 5.8. Parthasarathy et al. [52] look at how Vth

scales in networks of metal nanoparticle arrays with random threshold voltages ateach nanoparticle at finite temperatures. They assume that at a finite temperatureT a fraction of the barriers, due to the nanoparticle charging energies, p(T ) can beovercome by thermal fluctuations. These junctions are assumed to behave as ohmicjunctions. The fraction of barriers overcome by thermal fluctuations increases as Tincreases. When a certain fraction of the barrier can be overcome by the thermalfluctuations a conducting path is formed between the contacts. The fraction ofbarriers needed to be overcome is the percolation threshold of the array. The thresholdvoltage Vth for the conducting pathway is zero. In a two dimensional hexagonallyclose packed (hcp) array the threshold voltage is

Vth = VCBN(1 − 4.8kBT

pcEC

)(5.17)

with pc = 2 sin(π

18

), for an hcp array

where N is the number of molecular junctions spanning the gap between theelectrodes and Ec is the mean charging energy of the nanoparticles as calculated byEquation 5.1.

The other characteristic parameter of the model in Equation 5.16 is the exponentζ. The exponent takes the values 1 and 5/3 for one and two dimensional squarearrays, respectively [35, 47]. In recent work Šuvakov and Tadic [74] model the IVcharacteristic in two dimensional hexagonal arrays of nanoparticles. They find thatthe exponent ζ takes values of ζ ≈ 2.5 − 2.8 in weakly disordered hexagonally closepacked arrays. When quenched charge disorder is added to the array the exponentis reduced to ζ ≈ 1.3. In highly topologically disordered arrays the exponent takeshigher values ζ ≈ 3.9.

In the following section we estimate the value of the threshold voltage and theexponent from our measured data.

5.4. Measurements of two dimensional nanoparticle arrays at low temperatures 45

5.4 Measurements of two dimensional nanoparticle arrays at lowtemperatures

The transport through several devices was measured. First we will look at themeasurement results of a single device and see how to extract the threshold voltageVth and the exponent ζ. From the threshold voltage we get information about thecharging energy of the nanoparticles in the array, these values can be compared withtheoretical values calculated using the equations presented above. Furthermore, thethreshold voltage is useful to scale the measured data. By scaling the data, we see thatthe device fabrication and the measurement results are reproducible and the transportis not governed by size effects. Once the threshold voltage is known we can obtainthe exponent ζ. This exponent gives information about the disorder in the arrays, thiswill be discussed below.

Before we look at the data we can calculate typical values of the parameters weexpect in the measurements. The size of nanoparticles and interparticle spacing fabri-cated using the same protocol we use have been reported [9]. The nanoparticle radiuswas R ≈ 5 nm, and the interparticle spacing s ≈ 2.5 nm. The effective dielectricconstant of the octane monothiol molecules (S–C8) covering the nanoparticles wasreported as εr = 2.5 [9].

Using Equation 5.2 and the values for R, s, and εr from above, the capacitanceof a single nanoparticle is CNP = 1.4 aF. Using Equations 5.1 and 5.8 one can aswell calculate the charging energy of the nanoparticle Ec = 57 meV and the voltageneeded to overcome the Coulomb blockade VCB = 115 meV. When an array iscomposed of many such nanoparticles the effective capacitance of the nanoparticlesscales as shown in Equation 5.15 and the capacitance takes the value Cc

array = 4.2 aF.The superscript c is used to indicate a calculated value. This changes the effectivecharging energy which becomes Ec

c = 19 meV and the voltage to overcome Coulombblockade becomes VCB = 38 meV. At finite temperatures electrons can overcomethe Coulomb barrier by thermal excitations. Taking this into account the thresholdvoltage for conduction is scaled as shown in Equation 5.18 and becomes Vc

th = 28mV at a temperature of T = 4.2 K. Now we will look at the data and see how themeasured value of Vth compares with the calculated one.

5.4.1 Extracting a threshold voltage from the measured data

First we look at a single measurement of a single device. The sample was kept at atemperature of 4.2 K during the measurements. The device had a width of 410 ± 10nm and a length of 410 ± 10 nm, thus comprising of a N × M = (35 ± 2) × (35 ± 2)nanoparticle array. The voltage and current in all figures have been scaled to give thevalues per molecular junction as described in Section 5.3.1.

Figure 5.7 shows the measured IV curve. The measured curve has an S–shapesimilar to the calculated curve in Figure 5.6. The onset of conduction is not as clear in


Figure 5.7: An IV measurement of a typical device. The data shows an onset of conductance between 0and ±50 mV. Beyond the threshold voltage the current increases according to a power law. Thedashed lines indicate the threshold voltage for conduction. Their positions are extracted from thed2I/dV2 data, Figure 5.9

the measured data as in the calculated curve. The data shows an onset of conductionsomewhere midway between 0 and ±50 mV. Beyond the onset the current increasesaccording to a power law. Figure 5.8 shows the measured derivative of the IV curve,namely the dI/dV curve. The data shows a minimum around zero bias voltage. From0 V to around ±50 mV the differential conductance increases sharply, indicating anonset of conductance. The structure visible in the curve beyond ±50 mV will bedescribed later in the text. From Figures 5.7 and 5.8 it is clear that the onset ofconductance takes place between 0 and ±50 mV. The threshold voltage seems to havesome spread and it is hard to determine it exactly from these figures.

Looking at the measurement of the second derivative of the IV , shown in Figure5.9, there is a peak/dip between 0 and ±50 mV. The position of this peak/dip is wherethe steepest slope in the dI/dV is and is taken to correspond to the mean thresholdvoltage. Beyond ±50 mV are more peaks and dips. Those features will be discussedin detail in Chapter 6. From the d2I/dV2 data we extract a threshold voltage of Vm

th =

31 mV. The superscript m is used to indicate a measured value. This correspondsto a charging energy of Em

c ≈ 20 meV, the nanoparticle capacitance is Cm ≈ 4 aF.The measured threshold voltage agrees well with the calculated values, Vc

th = 28mV, as well as the charging energy Ec

c = 19 meV and the capacitance, Cc = 4.2aF. The observed difference in the measured and calculated capacitance comes fromvariations in R, s, and εr from the values stated above.

It is convenient to use the position of the highest peak and lowest dip in the d2I/dV2

data to estimate the position of the threshold voltage of the devices. The thresholdvoltage obtained from the peak/dip position can be thought of as a mean threshold


Figure 5.8: A dI/dV measurement of a typical device. The differential conductance has a minimum aroundzero bias. The differential conductance increases sharply when the applied bias changes awayfrom zero. This sharp increase in the conductance happens as the charge carriers overcomethe Coulomb blockade in the nanoparticles. The dashed lines indicate the threshold voltage forconduction. Their positions are extracted from the d2I/dV2 data, Figure 5.9

Figure 5.9: A d2I/dV2 measurement on a typical device. The highest peak and lowest dip on either side ofzero bias voltage correspond to the fast increase in the differential conductance shown in Figure5.8. The peak position corresponds to the mean threshold voltage to overcome Coulomb blockadeand the peak width corresponds to the distribution in energies sufficient to overcome the Coulombblockade. The dashed lines indicate the threshold voltage for conduction.


voltage. The width of the peak indicates that there is some distribution in the onsetof conductance in the device. The broadening of the peak in the d2I/dV2 will bediscussed in Section 5.5.

Using the method discussed above the threshold voltage of several devices wasmeasured. Table 5.1 summarises the results of these measurements. The table showsa device number composed of a sample number, first digit, and a device number,second digit. Seven devices on four samples were measured. The table shows thedimensions of the devices in units of nanoparticles. The arrays in the devices are Nnanoparticles long and M nanoparticles wide. The measured threshold voltage Vm

th isshown for each device. The measured threshold values compare well to a calculatedvalue of Vc

th = 28mV . The table also shows the values of the exponent ζ and a fittingparameter Gi, the details of these parameters are discussed in the following section.

Dev. N M Vmth [mV] ζ Gi [pS]

S1–D1 13 18 28.8 1.18 0.20S1–D2 23 31 26.4 1.20 0.14S2–D1 35 35 25.8 1.43 0.32S2–D2 37 88 24.6 1.32 0.09S3–D1 48 19 26.9 1.32 2.30S3–D2 40 90 30.5 1.33 0.21S4–D1 19 91 35.1 1.33 0.23

Table 5.1: The values obtained for the threshold voltage Vmth measured by the position of the highest/lowest

peak/dip in the d2I/dV2 data in seven devices on four samples. The devices measured arenumbered by two digits, the first digit indicates a sample number and the second a device number.The dimensions of the device are indicated in units of nanoparticles, the array in the device consistsof N × M nanoparticles. The measured threshold values compare well to a calculated value ofVc

th = 28mV . The exponent ζ is extracted from Figure 5.10. The parameter Gi is a fitting parameterused to have all IV curves in Figure 5.10 collapse on top of each other.

5.4.2 Determining the exponent ζ

When the threshold voltage is known it is time to inspect the ζ exponent in Equation5.16. The value of this exponent is related to the dimensionality of the nanoparticlearray [35, 47] and the disorder in the array [74].

Equation 5.16 shows that the current, above Vth, in the nanoparticle arrays shouldgrow in proportion with the applied voltage and the exponent ζ. It has been shown thatin arrays containing ∼ 103 nanoparticles size effects do not govern the conductance[74]. Assuming that the device fabrication is reproducible regarding disorder in thearrays and that the device conductance is not influenced by size effects, one wouldexpect the normalised current In = I/MVthGi to be identical in different devices.Where the measured current I is normalised by the number of nanoparticles spanning


Vn = (V − Vth)/Vth

I n=

I/M

VthG

i

ζ = 1.3

10−1

100

10110

−1

100

101

100

10110

−1

100

I n=

I/M

VthG

i

ζ = 1.3 ζ = 2 ζ = 5/3

ζ = 1

1.5Vth

0.5Vth

Vn = (V − Vth)/Vth

Figure 5.10: IV measurements on seven devices from four different samples are shown in the main figure.The current is scaled with 1/MVthGi where M is the number of nanoparticles in parallel in eachdevice, Vth is the threshold voltage for conduction in each device, and Gi is a scaling parameterused to make the curves collapse on each other. The slope of the curves at high voltages is fittedto get the exponent ζ. The black solid line shows a curve calculated using Equation 5.16 withζ = 1.3. The dotted lines are calculated using Equation 5.16 using the ζ values proposed byMiddleton and Wingreen [47] and have a slope of 5/3, and 1. The dash–dot line is calculatedby Equation 5.16 using ζ = 2 for weakly disordered arrays proposed by Šuvakov and Tadic[74] The inset figure shows a measurement of a single device. The figure shows that changingthe threshold voltage used to normalise the IV data does not influence the slope of the curve athigh bias voltages. The figure shows the same data normalised with different threshold voltages.The blue symbols show the data normalised with the measured Vth, the red symbols show thedata when a threshold voltage of 1.5Vth is used, and the green shows the data when a thresholdvoltage of 0.5Vth is used to normalise the data. The black lines show a calculated curve with andexponent ζ = 1.3.

the width of the device M, the threshold voltage Vth, and an initial conductance Gi.The initial conductance Gi is a fitting parameter used to have all the curves in Figure5.10 falling on top of each other. The values obtained from fitting Gi are displayed inTable 5.1. The inset in Figure 5.10 shows that changing the threshold voltage used tonormalise the data does not influence the slope of the data at high voltages. The figureshows the same data normalised with Vth plotted in blue symbols, normalised with1.5Vth plotted in red symbols, and normalised with 0.5Vth plotted in green symbols.

A straight line can be fitted to the measured curves at the high bias end of theplot. The resulting slope corresponds to ζ in Equation 5.16. The fitted ζ values forthe measured data in Figure 5.10 are shown in Table 5.1. The value obtained for theexponent is ζ = 1.3. These values are lower than 5/3 as proposed by Middleton andWingreen [47] for a two dimensional array, ζ = 5/3. Middleton and Wingreen [47]


calculate that the ζ value in a one dimensional array is ζ = 1. One might argue thatthe value for ζ = 1.3 obtained in the measurements indicates that the arrays behave asthough they are in an intermediate regime between purely one dimensional and purelytwo dimensional. This would suggest that the conductance paths in the array were amixture of paths confined to a chain of nanoparticles, and paths where electrons areable to meander and branch through a patch of nanoparticles.

A different explanation is offered by Šuvakov and Tadic [74], which calculate ζ =1.3 in topologically ordered arrays with quenched charge disorder. In the model thearrays have a small dispersion of cell sizes around the hexagonal structure and theyare locally homogeneous, with each node in the array having exactly three links. Thecharge disorder is uniformly distributed at each node and has a size of 0 ≤ qi ≤ 1e,e is the charge of a single electron [74]. The value they calculate corresponds to thevalues of ζ shown in Table 5.1. The quenched charging disorder could arise fromtrapped charges in the SiO2 substrate.

The ζ exponent has been measured by a few groups and the values obtainedvary. Elteto et al. [17] measured the transport in quasi one dimensional arrays ofAu nanoparticles. The average width of the array was 4 nanoparticles and the lengtharound 60 nanoparticles. They find ζ ∼ 1.4−2.6. They claim that these narrow arrayshave not yet reached the one dimensional limit and that their findings indicate that thecurrent paths are still able to meander and branch. In two dimensional arrays currentpaths are able to branch as more voltage is applied to the device the electrons haveenough energy to overcome higher barriers and can choose new paths. Furthermore,Parthasarathy et al. [52] find ζ = 2.25± 0.1 in two dimensional arrays of hexagonallypacked Au nanoparticles with 27–170 nanoparticles spanning the gap between theelectrodes and a width of ∼ 270 nanoparticles. Their value comes close to the valuesof ζ in weakly disordered arrays without charge disorder [74].

Liao et al. [45] investigate the influence of the substrate on ζ. They fabricateboth free–standing nanoparticle arrays and nanoparticle arrays on a substrate. Theymeasure a value of ζ = 2 for free–standing arrays and report there is a significantdifference in the exponent depending on whether the arrays are free standing or on asubstrate. They report ζ = 2.4 for arrays on a substrate. The claims made by Liaoet al. [45] support the idea that the substrate has an influence on the ζ exponent.

So far, measurements of the ζ exponent in several experiments have given an widerange of values. Theoretically, it has been predicted that the exponent depends on thedimensionality of the conducting paths in the arrays [47] as well as the topologicaland charging disorder [74]. Even though the range of values the exponent ζ can takehas been shown to depend on the topological and charging disorder of the array, theunderlying physical reason was not explained [74].

Charge disorder in the array would influence the threshold voltage for the onset ofconductance. The details of the peaks observed in the d2I/dV2 can give an indicationof whether charge disorder is present in the arrays. This will be discussed in thefollowing section.

5.5. Broadening of Coulomb blockade induced features 51

5.5 Broadening of Coulomb blockade induced features

In this section we look in detail at the peak/dips around ±Vth in the d2I/dV2 data.These peaks/dips were used in Section 5.4.1 to determine the value of the thresholdvoltage for conduction. These peaks/dips have a finite width. In this section we lookat what causes their broadening.

The broadening of a Coulomb blockade induced feature in the d2I/dV2 data canbe calculated as

Wjnct =

√W2

T +W2ac +W2

n +W2a +W2

q (5.18)

where Wjnct is the full width at half maximum (FWHM) of the measured peak. Thebroadening includes a thermal broadening term WT = 5.4kBT N/e [56], a term dueto the ac modulation used to measure the peak Wac, a broadening term Wn due to thedistribution in the nanoparticle capacitance, a term Wa due to topological disorder inthe array, and a term Wq due to charge disorder in the array. The broadening due to theac voltage applied to the junctions is calculated by convoluting a Gaussian peak by anac voltage and measuring the resulting broadening. The influence of the distributionin the nanoparticle capacitance is calculated as:

Wn =δVth

N(5.19)

where δVth is the error in the threshold voltage due to the distribution in the chargingenergy of the nanoparticles, and N is the number of nanoparticles spanning the gapbetween the electrodes in series. The broadening due to topological disorder in thearrays is found by:

Wa =Vth

N2 δN (5.20)

where δN is the error in the number of nanoparticles bridging the electrodes. The fullerror calculation is given in Appendix G. The broadening due to charge disorder inthe array can be calculated by looking how the energy of the nanoparticles changeswhen their charge changes as in Equation 5.3:

ΔU± =Q ± e)2

2C+

Q2

2C

The capacitance of the nanoparticle plays a role in how the energy of the nanoparticleschanges when the charge on them changes. The charge disorder is carried forwardto the charging energy of the nanoparticles and the threshold voltage. The full errorcalculation is in Section G.2 in Appendix G. We assume that the error values from thecalculations in Appendix G are the standard deviation σ of a Gaussian distribution.Thus, the full width at half maximum values are obtained by FWHM = σ2

√2 ln(2).


Figure 5.11: IV curves measured while an ac voltage of different amplitudes was added to the dc voltageapplied to the device. The figure shows that the IV response of the device is not influencedsignificantly by the ac voltage. When the amplitude of the ac voltage is at 64 mV per molecularjunction the onset of conductance around ± 30 mV dc bias is smeared out.

Of the terms contributing to the broadening only the amplitude of the ac voltageand the temperature of the sample can be easily controlled. In the rest of the sectionwe look at how these terms influence the broadening of the peaks.

First we look at the influence of the ac voltage on the peak width. Figures 5.11,5.12, and 5.13 show the influence of changing the amplitude of the applied ac voltageon the measured current, differential conductance and the second derivative of thecurrent, respectively. The influence of the ac amplitude on the IV measurementis minimal, except in the case where 64 mV ac is applied over each molecularjunction in the device. With this high ac voltage the onset of conductance abovethe threshold voltage is washed out in the IV curves. This is also evident whenone looks at the differential conductance in Figure 5.12. The dip around zero biasvoltage decreases monochromically with increasing amplitude of the ac voltage. Inthe second derivative of the current, Figure 5.13, the peak/dip at ±Vth is broadened,and lowered with increasing ac voltage. From Figure 5.13 a value of Vth ≈ 30 mVis found. The amplitude of the largest ac voltage used, 64 mV, is larger than twicethe threshold voltage. In the analysis of the data the measurement with this large acvoltage is omitted.

The values of the temperature broadening, broadening due to a distribution in thenanoparticle capacitance, broadening due to topological disorder, and charge disordershould all be constant in the device at low temperatures. These broadening values canbe calculated and have values of WT = 5.4kBT/e = 2.0 mV, Wn = 9.1 mV, Wa = 7.6mV. The broadening due to charge disorder cannot be calculated directly, since it isimpossible to know the exact charge disorder.


Figure 5.12: dI/dVmeasurement of the same device as the IV measurement shown in Figure 5.11. The zerobias conductance increases as the amplitude of the ac signal increases. Furthermore, the featuresin the dI/dVvisible beyond the Coulomb blockade are smeared out with increasing amplitude.

Figure 5.13: The d2I/dV2 measurement of the same device as the IV measurement shown in Figure 5.11.The curves are measured using different amplitudes of the ac voltage applied to the device. Mostnotably the amplitude and the broadening, of the peak around ±30 mV dc bias, decrease andincrease, respectively. Features in the curves measured beyond the Coulomb blockade region,peaks on the positive dc bias side and dips on the negative side, are most prominent when theamplitude of the ac voltage is between 14 and 22 mV. Below 14 mV the signal is barely abovethe noise threshold, above 22 mV ac amplitude smearing of the features starts being apparentand at 64 mV the features are completely washed out.


V 2ac [mV2]

FW

HM

2[m

V2]

200 400 600 800 10001000

2000

3000

4000T = 4.2 K

Figure 5.14: The full width at half maximum of the Coulomb induced feature around ± 30 mV dc bias inFigure 5.13. The black dotted line is the calculated full width at half maximum by the thermalbroadening, the broadening due to the ac voltage applied to the device, the broadening due tothe distribution in nanoparticle capacitances, and the broadening due to topological disorder.The black solid line is the calculated broadening with a broadening term Wq = 30 mV added toit. This extra broadening in the peak is assumed to come from the charge disorder in the array.The shaded area represents the error of the calculated broadening, the black line. The width ofthe shaded area comes from the error of the number of nanoparticles in the conducting path and±10% of the measured broadening.

Figure 5.14 shows how the broadening squared evolves as the amplitude of theapplied ac voltage squared. The black dotted line is the calculated broadening usingEquation 5.18 and the broadening values mentioned above, but Wq = 0 at this point.The broadening due to the ac voltage is calculated by convoluting an Gaussian peakwith an averaging filter of a length equivalent to the amplitude of the ac voltage. Theblack dotted line is the lowest expected broadening. The black solid line is the sameas the black dotted line, but with an extra broadening term W = 30 mV added to it.Setting this extra broadening term as Wq one can estimate the charge disorder in thearrays. Following the error calculations in Section G.2 in Appendix G the resultingdistribution in the charges on the nanoparticles is ΔQ = 0.19e. The shaded area isfound from the error on the number of nanoparticles spanning the length of the deviceand a ± 10% measurement error of the peak broadening.

The broadening of the Coulomb blockade induced features in the d2I/dV2

measurement were also measured as a function of temperature for the temperaturerange from 4.2–300 K, Figure 5.15. The peak evolves in a similar manner withincreasing temperature as it did with increasing ac voltage, that is the peak heightdecreases while its width increases. Figure 5.16 shows the broadening squared plottedas a function of the temperature squared. The main figure shows the data plottedon a log–log scale to emphasise the low temperature values. The inset shows the


0 50 100 1500

2

4

6

8

10

12

Vjnct [mV]

d2I/dV

2[×

10−11AV

−2]

Vac = 20 mV

4.2 K4.4 K6.6 K17 K84 K295 K

Figure 5.15: The d2I/dV2 measurement of the same device as the IV measurement shown in Figure 5.11.The d2I/dV2 signal is measured at different sample temperatures. The measurement shows asimilar trend as the measurement shown in Figure 5.13 where the amplitude of the ac voltagewas varied. The amplitude decreases as the temperature increases while the full width of thepeak at half maximum increases with temperature.

data on a linear scale. The black dotted line is the calculated broadening using theknown broadening parameters, Wq = 0 since it is unknown. The broadening perjunction Wjnct, black curve in Figure 5.16, was calculated using Equation 5.18 andthe same parameters for Wn, and Wa as above. The broadening due to the 20 mVac voltage was found to be Wac = 34 mV, which corresponds to the same width aswas used above in Figure 5.14. An extra broadening term W = 35 mV is added tothe calculated broadening. We assume that this extra broadening term correspondswith the broadening due to the charge disorder Wq. This corresponds well with themagnitude for this broadening term obtained when the amplitude of the ac voltagewas increased. There it was 30 mV. Broadening due to charge disorder of a magnitudeWq = 35 meV, corresponds to a distribution in the charge on the nanoparticles ofΔQ = 0.23e. The black line shows the calculated values of the broadening withWq = 35 mV. The shaded area represents the error in the calculation

The charge distribution on the nanoparticles extracted from the measurementwhere the amplitude of the ac voltage was varied and the measurements wherethe temperature of the sample was varied agree well with each other. The chargefluctuations calculated ΔQ = 0.2e is with in reasonable bounds and might indicatethat charge disorder does play a role in the transport through the devices.


Figure 5.16: The full width at half maximum of the Coulomb induce feature around ± 30 mV dc bias inFigure 5.15. The main figure and the inset show the same data. The main figure shows thedata on a double logarithmic scale to emphasise the points measured at low temperatures. Theinset shows the data on a double linear scale. The black line shows the calculated broadeningusing Equation 5.18 setting the broadening due to charge disorder Wq = 35 mV. The grey arerepresent the error in the calculated broadening. The black dotted curve is the same as the blackcurve, but with the broadening due to charge disorder Wq = 0 mV. This is the lower limit of thepossible broadening.

5.6 Summary

In this chapter we have introduced a model for the transport through a double tunneljunction. The model characterises the transport through a nanoparticle coupled toan electrode on either side of it via tunnel junctions. To describe the transport in anarray of nanoparticles, building on this model, we investigated how the topology ofthe nanoparticle array affects the voltage drop over each junction and the currentflowing through it. The effects of the environment on the charging energy of ananoparticle were discussed and the influence of temperature on the transport througha nanoparticle array.

We looked at how to extract the threshold voltage for conductance from ourmeasurements. Using the extracted threshold voltage we could rescale the data andfit it to a model where an exponent in the model describes the topology of the arrayas well as the disorder in the array. Two distinct disorders play a role, the topologicaldisorder and the charge disorder in the array.

5.6. Summary 57

Looking into the broadening of features arising from Coulomb blockade in thenanoparticle arrays. Several parameters causing broadening can be estimated fromerror calculations while others can be calculated directly. When comparing the sum ofall the known broadening parameters to the measured broadening it is evident that thecalculated broadening is smaller than the measured one. Assuming this broadening,which is unaccounted for, stems from the charge disorder we calculate the fluctuationsin the nanoparticle charges that would cause broadening of that magnitude.

Chapter 6The influence of molecules on transport inthe nanoparticle arrays

6.1 Introduction

In Chapter 5 we looked at how nanoparticles influence transport in the nanoparticlearrays at low temperatures. From measurements done at room temperature we alsoknow that the molecules present in the nanoparticle arrays contribute to the transport[43]. Not only do the molecules in the array contribute to the transport, but even theoxidation state of the molecules plays a role. As discussed in Chapter 3 the functionof a nanoparticle array device can be determined by the function of the moleculesin it, at room temperature. In this chapter we will look at the contribution of themolecules in the array to the transport at low temperatures.

Molecular vibrations, phonons, can contribute to the conductance of a metal–molecule–metal junction. The effect is known as inelastic electron tunnelling.Inelastic electron tunnelling spectroscopy (IETS) through a molecular junction wasfirst performed on metal–metal oxide–metal structures where a thin layer of organicmolecules had been deposited on the metal oxide [32, 39]. How the electron–phonon interaction influence the conductance of the metal–molecule–metal junctionis determined by the junction conductance [1, 14, 21, 53, 55, 65, 72]

Thirty years after the experiment by Jaklevic and Lambe [32], Stipe et al. [64]could distinguish between hydrogen and deuterium in a single acetylene (C2H2) and adeuterated acetylene (C2D2) molecule on a copper surface using a scanning tunnellingmicroscope (STM) in ultra high vacuum. The distinction was made by measuringthe vibrational energy of the C–H and C–D stretch modes in the C2H2 and C2D2

molecules, respectively. Since the first IETS measurements several research groups

59

60 The influence of molecules on transport in the nanoparticle arrays

have started working on measuring IETS in junctions containing a single molecule.Until now, the methods used to measure IETS are: STM break junction [1, 4, 27,28, 41, 50, 51, 58], mechanically controllable break junction [15, 65, 66], cross wirejunction [6, 38], and electromigrated junction [63]. To our knowledge no one hastried to measure IETS in devices comprising of a collection of molecular junctions,such as a nanoparticle arrays.

As discussed in Chapters 2 and 3 nanoparticle arrays are a highly versatile platformfor molecular electronics. They offer the possibility of investigating how a moleculeresponds to its environment. The properties of individual molecules have been shownto define the transport through the nanoparticle arrays. In particular, the conductanceof a nanoparticle array can be changed by illuminating a photo–sensitive moleculeto change its conformation [73] or the conductance can be changed by altering theoxidation state of a redox–active molecule [42]. The ability to probe the phononmodes of a molecule before and after such treatment would be of great interestto the molecular electronics community. This would open up the possibility tomeasure a unique fingerprint of the molecules taking part in the electrical transport inthe devices and distinguish between different molecular conformations or oxidationstates. Current methods used to measure IETS of molecules do not offer the sameflexibility of device treatment as the nanoparticle arrays do.

Previously infrared spectroscopy has been used to identify the molecules presentin the nanoparticle arrays [9]. The position of the maximum in UV–vis absorptionspectroscopy has been correlated with the conductance of the molecules in the arrays[9, 73]. The next step could be to detect the structure of the molecules taking part intransport directly with IETS.

Measuring the contribution of vibrational modes of individual molecules within anarray of nanoparticles is a challenging task. As discussed in Chapter 5 we know thatdisorder in the array itself would cause the voltage drop over each molecular junctionto vary, thus causing broadening of peaks or even the same peak to appear at morethan one voltage. The coupling between the electrodes and the array could causethe IETS to be non–symmetric. So far symmetry has been used to identify IETSpeaks among peaks in the d2I/dV2 caused by other sources [4, 27]. The rewardsfor overcoming the challenges are a better understanding of the transport throughmolecular devices based on nanoparticle arrays and yet another tool to identify themolecular contribution to the transport in the arrays.

6.1.1 A general description of IETS

The transport through a molecule can be influenced by the electron–phonon (e–ph)interactions during charge transfer. In low conducting junctions G � G0, whereG0 = 2e2/h is the conductance quantum, the conductance in the junction is enhancedby the e–ph interaction. The electron is scattered inelastically forward and it is saidthat an inelastic conductance channel opens up. The increase in conductance due to

6.1. Introduction 61

Figure 6.1: (a) Inelastic electron tunnelling becomes possible when an electron tunnelling through amolecule has enough energy eV to excite a vibrational mode, phonon of energy �ω, in themolecule. In a low conducting junction G � G0 the electron is scattered forward and theconductance of the channel increases. (b) The increase in conductance is observed as a kink inan IV measurement, a step in the dI/dV measurement, and a peak in the d2/dV2 measurement ofthe junction. The peak positions in the d2I/dV2 give a spectrum of the energies of the molecularphonon modes contributing to transport.

forward scattering of electrons by phonons is on the order of ∼ 1% [4, 18], althoughan increase as high as 10% has been reported [28]. Since inelastic electron tunnellingcauses an increase in conductance it is observed as a kink in the IV measurement,a step in the dI/dV measurement, and a peak in the d2I/dV2 measurement, asillustrated in Figure 6.1. The dc part of the current signal corresponds to the currentflowing in the device, the first harmonic of the current signal corresponds to thedifferential conductance of the device, and the second harmonic of the current signalcorrespond to the second derivative of the current in the device. The detailed Taylorexpansion of the current is given in Appendix F. The peak positions in the d2I/dV2

measurement give a spectrum of the molecular phonon energies which contributeto transport. This transport spectroscopy is known as inelastic electron tunnellingspectroscopy.

The phonon modes of a molecule can be measured by other means, in particularinfrared (IR) and Raman spectroscopy. The main advantage of IETS over IR andconventional Raman spectroscopy is the sensitivity of IETS. While IR and Ramanspectroscopies require 103 or more molecules to provide a spectrum, IETS can bedone on a few molecules trapped between a pair of electrodes [59]. IETS can also beused to determine whether a certain molecule is present in a molecular junction andcontributing to the transport.

While the phonon modes observed by IR and Raman spectroscopy are governedby well known selection rules, there are no strict selection rules for IETS [51, 59].Instead of selection rules, a set of propensity rules has been set forward and used asguidelines to help determine which phonon modes are expected to take part in thetransport. These rules imply that the most important phonon modes to transport are


those that are along the most active conduction paths of the molecule. Symmetricmodes are usually more active than others [68, 69]. The majority of the measuredIETS signal is attributed to a few phonon modes at high energies [19]. In practise,the low energy modes are masked by a zero bias feature caused by scattering in theleads, Coulomb blockade, and other processes [79].

6.1.2 A general IETS measurement of a nanoparticle array device

The IETS of the nanoparticle array device was measured at 4.2 K using the setup described in Chapter 4. Two SR830 Lock–in amplifiers were used during themeasurement. One supplying an ac voltage to the sample and measuring the 2ndharmonic of the resulting signal, the other measuring the 1st harmonic of the signal.The measurement was performed by applying a voltage, comprising of a dc part andan ac part, to a device. The dc voltage was increased in small steps, normally onetenth of the amplitude of the ac voltage. Before measuring at each dc voltage wewaited until the device and measurement circuit reached steady state. The time forthe measurement circuit and device to reach steady state was normally ∼ 21 sec forthe Lock–in amplifier at 73 Hz with a 12 dB/Oct filter, and a time constant of 3 sec.Normally 400 measurements were performed at each dc bias. The mean value of the400 points was used as the measured value. This method was preferred, to increasethe signal–to–noise ratio, over many voltage sweeps. A normal measurement takes3–8 hours.

In Section 5.4.1 we looked at an example of a transport measurement in a singledevice and saw how to locate the threshold voltage Vth using peaks in the d2I/dV2

measurement. The device was fabricated using the protocol described in Section4.2. The nanoparticles were coated with S–C8, (S(CH2)7CH3), molecules. Themeasurement was done by sweeping the voltage from 0 – 200 mV, from 200 – −200mV, and from −200 – 0 mV. Using the same measurement data again, now we lookat the features beyond Vth. Figures 6.2, 6.3, and 6.4 show the same data as in Section5.4.1, IV , dI/dV , and d2I/dV2 respectively, the background has been colored toemphasise the features we are interested in. Looking at the d2I/dV2 measurementin Figure 6.4 working our way from 0 V: The red area represents an area dominatedby the Coulomb blockade; The yellow area emphasises a feature which appears astwo peaks on the positive voltage side. On the negative voltage side there is a strongdip there when scanning the voltage from 0 – −200 mV, but it does not appear whenscanning the voltage from −200 – 0 mV; The green area emphasises strong peaks/dipssymmetric about 0 voltage. The increase in conductance in this area causes a clearlyvisible step in the dI/dV measurement. The blue area shows two peaks/dips whichappear at positive and negative voltage.

In Figure 6.4 it is evident that the fine structure of the measurement is notsymmetric around 0 V, and that scanning twice over the same voltage does notnecessarily give the same exact result. The origin of the asymmetry will be discussed


Figure 6.7: A schematic illustrating how an applied bias voltage Vb drops over a double junction comprisingof a nanoparticle between two electrodes. A schematic of the junction is shown in figure (a). Theschematic shows how the threshold voltage is overcome at the same applied bias voltage Vb whenthe voltage is applied to Electrode 1, figure (b), or Electrode 2, figure (c). The voltage drops overtwo junctions: A factor η1 of the applied voltage drops over the junction between Electrode 1 andthe nanoparticle, NP; A factor η2 = 1 − η1 drops over the junction between NP and Electrode 2.

Figure 6.7 shows a simple model on how the voltage drops over a double junction.A nanoparticle, NP, is trapped between two electrodes. The junctions are assumedto be asymmetric in the sense that a portion of the applied voltage η1 drops overthe junction between Electrode 1 and a nanoparticle NP. A portion η2 = 1 − η1

drops over the junction between Electrode 2 and NP. In order for conduction to startthe voltage drop over each junction needs to exceed a threshold voltage Vth. Eventhough the junctions are asymmetric the bias voltage Vb needed to overcome thethreshold voltage is the same, regardless whether the voltage is applied to Electrode1 or Electrode 2. The voltage needed for conduction to start is:

Vth ≤ |Vb|min(η1, η2) (6.1)

The nanoparticles are coated with molecules. These molecules bind to the Aunanoparticles with a thiol group giving a strong chemical bond. The electrodes,on the other hand, have no molecules attached to them. It is reasonable to assumethat the energy levels associated with the molecules are pinned more strongly to thenanoparticles than the electrodes. To make things simple, we assume that the energylevels of the molecules fully follow the energy levels of the nanoparticle. In this casethe schematic in Figure 6.8(b) shows how a phonon mode of energy �ω is not excitedwhen a bias voltage Vb is applied to Electrode 1. Figure 6.8(c) on the other hand,shows how the phonon mode is excited when the bias voltage is applied to Electrode

6.3. Broadening in peaks beyond the threshold voltage 67

Figure 6.8: A schematic illustrating how a voltage drops over a double junction comprising of a nanoparticlecoated with an organic molecule and placed between two electrodes. The structure of the junctionis shown in figure (a). The schematic shows how a phonon mode with energy �ω is not excitedwhen a bias voltage Vb is applied to Electrode 1, figure (b). If the bias voltage is applied toElectrode 2 the phonon mode is excited, figure (c).

2.We have attempted to describe, by a simple model, why the contribution of inelastic

electron tunnelling might appear at asymmetric positive and negative bias voltages inthe nanoparticle array devices. We contribute the asymmetry in the inelastic transportto asymmetric coupling between the nanoparticle array and the electrodes. A morerigorous model of asymmetry in inelastic tunnelling processes has been developed[20]. It describes how, at low bias voltages far from resonance with HOMO or LUMOof the molecule, the inelastic processes contributing to the transport can becomeasymmetric while the elastic processes are symmetric. The asymmetric contributionof the inelastic processes is not visible in the IV response since the contribution isso small compared to the contribution of the elastic processes. Asymmetric IETSspectra have been measured in single molecular junctions [57, 66]

6.3 Broadening in peaks beyond the threshold voltage

We have seen in Section 6.1.1 that it is possible to measure peaks in the d2I/dV2

beyond the Coulomb blockade. Before looking at IET spectra measured in the arrayswe look at the broadening in peaks beyond the threshold voltage. The measurementswere performed on a different sample than the measurements shown in Section 6.1.2.

Looking at the d2I/dV2 at voltages beyond the threshold voltage small peaks canbe observed. Figure 6.9 shows a close up of two such peaks, the inset shows thed2I/dV2 data from the whole voltage scan. Comparing the positions of these peaks,


−300 −250 −200 −150 −100−30

−25

−20

−15

−10

−5

0

Vjnct [mV]

d2I/dV

2[×

10−12AV

−2]

−100 0 100 200

−100

50

0

50

100

Vjnct [mV]

d2I/dV

2[×

10−12AV

−2]

Figure 6.9: A detailed measurement of two peaks beyond the threshold voltage. The dc bias voltage isnegative in the measurement so the dips in the measurement around −120 mV and −180 mVcorrespond to peaks while positive voltage is applied to the device. The inset shows the fullmeasurement of the d2I/dV2 of the device.

around −120 meV and −180 meV, with the known peaks for S–C8 in Table H.1 inAppendix H one can see that they appear at similar energies as the C–C stretch and aCH2 wagging and CH2 twisting phonon modes.

The broadening of these peaks as a function of applied ac voltage is shownin Figures 6.10 and 6.11. Figure 6.10 shows the two peaks after an exponentialbackground has been removed from the measured signal and the sign of themeasurement in Figure 6.9 reversed. Gaussian curves have been fitted to each peak,blue dotted curves, and the sum of the two Gaussian curves is also plotted on thefigure in a black dotted line. The measurement of the peaks is performed at 12,16, 20, 24, 28, and 32 mV ac amplitude. Figure 6.11 shows the full width at halfmaximum of the Gaussian fits in Figure 6.10. The red marks correspond to the peaksaround −120 mV and the blue marks correspond to the peaks around −180 mV. Theblack line is the model broadening given by [37, 39, 41]:

Wjnct =

√W2

T +W2ac +W2

a (6.2)

where WT = 5.4kBT = 2 mV is the thermal broadening, Wac = 1.7Vac isthe broadening due to the applied ac voltage, and Wa = VdcδN/N = 8 mV isthe broadening due to the topological disorder in the array, N is the number ofnanoparticles spanning the gap between the electrodes in series, δN is the error in thenumber of nanoparticles in series bridging the electrodes as calculated by EquationG.7 in Appendix G. The grey area indicates the error due to the error of the numberof nanoparticles bridging the electrodes and ±10% error on the fit of the FWHM. The

6.3. Broadening in peaks beyond the threshold voltage 69

Figure 6.10: Fits of Gaussian peaks to the d2I/dV2 in a single device taken at 12 mV, 16 mV, 20 mV, 24mV, 28 mV, and 32 mV, reading the figures from left to right and top to bottom. The peaks inthe figure correspond to the two peaks shown in Figure 6.9 with the background removed. Thebackground is determined by fitting an exponential function to the peak around the thresholdvoltage of the measurement taken with 12 mV ac amplitude. The peak is fitted to the curvebetween 30% and 80% of the peak height. The same background is used to subtract from all themeasurements. The blue curves in the figure show the two individual Gaussian peaks fitted tothe measurement and the black curve is the sum of the two blue curves.


V2ac [mV2]

FW

HM

2[m

V2]

T = 4.2 K

200 400 600 800 1000 1200

500

1000

1500

2000

2500

3000

3500

Figure 6.11: The full width half maximum values of the peaks shown in Figure 6.10. The red markscorrespond to the peak around −120 mV, and the blue marks correspond to the peak around−180 mV. The FWHM values are extracted from the Gaussian peaks fitted in Figure 6.10. Theblack line is calculated using the Equation 6.2, with WT = 2 mV and Wa = 8 mV. The grey arearepresents the error in the calculated broadening.

three broadening factors WT, Wac, and Wa account for all the observed broadeningin the peaks. We assume that each peak is a sum of several peaks, correspondingto several phonon modes, but we cannot resolve them due to the broadening of themeasurement.

In this section we discussed a source of broadening in the IETS signal observedin the nanoparticle arrays. The major source of broadening comes from the appliedac voltage and the topological disorder in the arrays. Now we have seen that it ispossible to observe the influence of inelastic electron tunnelling on transport in thearrays. The question still remains: Is it possible to identify the molecules present inthe arrays from the measured IETS signal?

6.4 Systematic IETS measurements of nanoparticle arrays

In Section 6.1.1 we saw that it is possible to measure IETS peaks in the nanoparticlearrays. We also saw that looking at a single measurement is not enough to determinewhere the peaks are positioned. There is disorder in the peak positions and twoconsecutive sweeps do not necessarily have the same fine structure. In Section 6.3we saw that the major contribution to the broadening in the IETS peaks is due tothe ac voltage and topological disorder in the nanoparticle arrays. In this sectionwe discuss how we can try to map out the true IET spectrum of the molecules wemeasure by measuring the d2I/dV2 response of the devices several times and findthe most probable peak positions in the data. The measurements in this section were

6.4. Systematic IETS measurements of nanoparticle arrays 71

Figure 6.12: IETS measurements of a nanoparticle array device, the absolute value of the imaginary partof the d2I/dV2 is plotted. The nanoparticles are coated with a S–C8 molecule. The top figureshows a single measurement. The black dots show an example where peak positions werechosen on the curve. The figures show that the IETS measurement is not symmetric aroundzero bias voltage. Furthermore, sweeping the bias voltage from 0 V to 220 mV does not givethe same fine structure in the data as sweeping the bias voltage from 220 mV to 0V. The lowerfigure shows 10 consecutive measurements. The voltage is swept from 0V to 220 mV, from 220mV to −220 mV, and from −220 mV to 0V in each measurement cycle. The results do showsome similar features, although the detailed features of each cycle vary. The amplitude of the acvoltage was 14 mV per molecular junction during the measurement. The curves are shifted upfor clarity.

performed on a different device than the measurements in Sections 6.1.2 and 6.3.Figure 6.12 shows the absolute value of the imaginary part of the d2I/dV2 signal

measured in a nanoparticle array device. The imaginary part of the d2I/dV2 signalhas the information about the change in differential conductance due the changein tunnelling rates as a function of voltage, as described in Appendix F. Here we


choose to look at the absolute value of the imaginary part of the signal since it isconvenient to compare peaks to peaks, at negative and positive bias voltages, withthe eye. The nanoparticles were coated with a S–C8 molecule. The top figure showsone measurement cycle. The dc bias voltage was swept from 0 V to 220 mV, from220 mV to −220 mV, and from −220 mV to 0mV. The data in the figure are notsymmetric around 0 V bias and sweeping the voltage from 0 V to 220 mV does notgive the same fine structure as sweeping the voltage from 220 mV to 0 V. In orderto determine which peaks are coming from vibrational modes of the molecules andwhich peaks stem from other sources 10 measurement cycles were performed. Thelower figure shows the results of the 10 measurement cycles. In the 10 measurementcycles some features seem to appear more often than others. Below we discuss howwe can use the information in the 10 measurement cycles to determine which peaksare most likely to appear.

To probe which peaks are specific to the molecule in the array we performedmolecular place–exchange on the device measured above. If the molecule is trulycontributing to the d2I/dV2 signal, two different molecules should have differentcontributions. In that respect we replaced the S–C8 molecule, containing only C–C bonds between carbon atoms, with a S–OPE–S molecule, containing C–C, C=C,and C≡C carbon–carbon bonds. The structure of the molecules is shown in Figure6.14. Figure 6.13 shows the absolute value of the imaginary part of the d2I/dV2

measurement on the same device as in Figure 6.12. Before this measurementwas performed the device was slowly warmed to room temperature, taken out ofthe dipstick, and molecular place–exchange was performed on it overnight. Aftermolecular place–exchange the device was placed in the dipstick again and cooledto 4.2 K. After molecular place–exchange the features due to Coulomb blockadebecome sharper after each measurement cycle, as is seen in the Figure 6.13. Weinterpret this as rearrangement of the nanoparticles. It is possible that duringmolecular place–exchange the nanoparticles were able to move out of equilibrium.Furthermore, the molecules inserted into the nanoparticle arrays during molecularplace–exchange are dithiolated and can interlink two neighbouring nanoparticles[44]. It is possible that by interlinking the nanoparticles strain is induced in the arraythat relaxes when current flows through it. As discussed above disorder in the arraywould cause broadening of the peaks. It is unlikely that it would cause new sharppeaks to appear.

There are more peaks observed for the S–OPE–S molecule than the S–C8molecule. There are several reasons for this. One reason why there are more peaksin the S–OPE–S measurement is that the molecule has more possible phonon modesthan the S–C8 molecule. Furthermore, since the S–OPE–S molecule is a stiff rod likemolecule with the option to bind to two neighbouring nanoparticles, it is probablethat it is strained in the junctions. It has been shown that due to strain peak positionsin an IET spectra can be shifted by about 5 meV/Å [4]. When S–OPE–S moleculesare brought close together a π−π coupling can influence the transport through it [77].


Figure 6.13: IETS measurements of a nanoparticle array device, the absolute value of the imaginary part ofthe d2I/dV2 is plotted. The nanoparticles are coated with a S–OPE–S molecule. The top figureshows a single measurement. The figures shows that the IETS measurement is not symmetricaround zero bias voltage. Furthermore, sweeping the bias voltage from 0 V to 220 mV doesnot give the same fine structure in the data as sweeping the bias voltage from 220 mV to 0V.The lower figure shows 10 consecutive measurements. The voltage is swept from 0V to 220mV, from 220 mV to −220 mV, and from −220 mV to 0V in each measurement cycle. Theresults do show some similar features, although the detailed features of each cycle vary fromcycle to cycle. The amplitude of the ac voltage was 7 mV per molecular junction during themeasurement. The curves are shifted up for clarity.

It is unknown how this coupling would influence the IET spectra of the molecules.Finally, the measurement of the S–C8 molecule was done with 14 mV ac appliedto each junction while the measurement of the S–OPE–S was done with 7 mV perjunction. This means that the resolution in the S–OPE–S measurement is better thanin the S–C8 measurement.


One way of quantifying the probability of a peak appearing at a certain dc biasvoltage is to identify the positions of each peak in each curve and use them to build apeak–position probability–density function (PDF) [4]. The black dots in Figure 6.12show an example of selected peak positions in the scan from 0 – −220 mV. The PDFis obtained by summing up Lorentzian functions centered at each peak position Vpeaks.The PDF is described by

f (Vdc) =∑peaks

ε/π

(Vdc − Vpeaks)2 + ε2, (6.3)

where the width of the peak is taken to be ε =√

(5.4kBT )2 + (1.7Vac)2/10. Two PDFsare generated, one for the positive bias voltages and one for the negative bias voltages.The PDFs are normalised so that the highest peak in the two PDFs is equal to one.The purpose of the PDFs is to show at which dc bias voltages the peaks appear. Theyare not intended to indicate the height of each peak, thus the contribution of eachphonon mode to the transport cannot be quantified using theses plots.

Figure 6.14 shows peak–position probability–density plots of the IETS peaks forthe two measured molecules, S–C8 and S–OPE–S. The red and blue dots indicate,respectively, dip positions on the negative voltage side and peak positions on thepositive voltage side in the d2I/dV2 measurements in Figures 6.12 and 6.13. Thered and blue lines show the probability of a peak appearing at a certain dc voltage,calculated using Equation 6.3. The curves are normalised so that the highestprobability of the negative voltage or the positive voltage curve is equal to one. Theblack solid lines show the mean value of the d2I/dV2 curves. A separate mean valueis calculated for the curves at negative biases and positive biases. Next to the PDFfigures are schematics of the two molecules measured. The grey areas indicate theregions where phonon modes are known to be active [54]. The width of the grey areasis set to be equal to the calculated beak broadening Wjnct = 14 mV.

The PDFs in Figure 6.14 show a clear difference in the peak positions observedfor the S–C8 and the S–OPE–S molecules. The grey areas show reported values ofphonon modes active in the transport of similar molecules to the ones we measure,namely S–C11 and S–OPE–S [54]. Although candidate phonon modes are indicatedin the figures further investigations are needed to gain a clear IET spectrum. Acomprehensive list of known phonon modes for alkane molecules is available inAppendix H.


Figure 6.14: Peak–position probability–density plot of the peak positions obtained from Figures 6.12 and6.13. Red and blue dots indicate the positions of peaks observed in the figures. Red valuesindicate the position of dips on the negative voltage side and blue values indicate the positionof peaks on the positive voltage side. The red and blue lines show the PDF as calculated byEquation 6.3 of the peaks indicated by the red and the blue dots, respectively. The black linesshow the mean IETS signal of the 10 cycles shown in Figures 6.12 and 6.13. A separate meanis calculated for the negative and positive voltage sides. The molecular structures of the twomolecules measured are shown next to the PDFs. The grey areas indicate phonon modes ofsimilar molecules, S–C11 and S–OPE–S, proposed by Paulsson et al. [54]. The width of thegrey areas equals the calculated broadening Wjnct = 14 mV.


6.5 Conclusions

In this chapter we have looked at whether it is possible to measure IET spectrain the nanoparticle array devices. We found that there are peaks in the d2I/dV2

measurement beyond the threshold voltage and those peaks are most probably dueto scattering of electrons on phonons in the molecules in the devices. Thesepeaks appear at non–symmetric dc voltages about 0V. We attribute this observedasymmetry in the d2I/dV2 data to asymmetry in the devices, where the nanoparticlearrays contact the metallic electrodes on each side in an asymmetric manner. Thebroadening of the IETS peaks can be accounted for by the thermal broadening,broadening due to the applied ac voltage, and the broadening due to the topologicaldisorder in the arrays. Doing several measurements of the same device and collectingthe observed peak positions into peak–position probability–density plots might helpidentify the molecules in the devices.

We showed that it is possible to distinguish between two molecules in the arrays.Measuring two different molecules, before and after molecular place–exchange, in thesame device gave different spectra. It is however difficult to assign vibrational modesto the observed peaks and identify the molecule or components of the molecule usingthe measured spectra.

In spite of the disorder in the arrays we were able to measure the influence ofthe molecular vibrations on the transport through the nanoparticle arrays. Thisconfirms our former findings that the transport through the array is determined bythe individual molecules bridging the nanoparticles [42, 73]. Our findings indicatethat although challenging, IETS might be one more tool in our already extensivespectroscopic toolbox and could be useful to gain access to the finer details of themolecular contribution to the transport in our devices.

Chapter 7Conclusions and outlook

We have shown that at room temperature the transport through our nanoparticlearray devices can be tuned with the oxidation state of a redox–active moleculeinserted in the arrays. The devices showed a significant increase in conductanceafter oxidation of the molecule. The conductance was restored close to the startingconductance by reducing the molecule back to its neutral state. The tuning of thedevice conductance by oxidation and reduction could be repeated several times inthe same device. These measurements show that our devices are an interestingplatform for molecular electronics where the function of the device is defined bythe molecules in it. The function of the molecules is preserved even when they havecontacted the nanoparticles and the devices are shown to withstand several cycles ofa treatment with organic solvents without losing their function. These measurementswere discussed in Part I.

Until now, the width of the nanoparticle arrays has been controlled by patternedPDMS stamps and the distance between the electrodes was controlled by the distancebetween openings in a TEM grid. This method of patterned PDMS stamps and TEMgrids to define the device geometry is limited in flexibility. To gain more precisecontrol over the nanoparticle array geometry a new method had to be developed.

We developed a way of patterning the device on top of a SiO2 substrate using e–beam lithography. We can adjust the device geometry to our needs. By first depositingthe electrodes and an etching mask, then etching away the SiO2 around the electrodesand leaving a small area of SiO2 between them. The nanoparticle arrays were thentransferred on top of the structures with an unstructured PDMS stamp. Gaining thislevel of control over the array dimensions was challenging but we were rewardedwith the possibility of investigating the transport through the arrays in more depththan ever.

77

78 Conclusions and outlook

We chose to use our small nanoparticle arrays to investigate the non–lineartransport through our devices. We were interested in separating the contributionfrom the nanoparticles and the molecules to the transport. To do this we performedtransport measurements on our devices at liquid He temperatures.

We were able to measure the influence of the Coulomb blockade, due to the smallsize of the nanoparticles, on the transport. At higher bias voltages we saw evidence ofthe contribution of molecular vibrations to the transport. By doing molecular place–exchange on a single device we observed different signatures of the vibrational modesof the individual molecules to the transport. We can now quantify the disorder in thearrays and determine its contribution to the transport. This was discussed in Part II.

7.1 Outlook

Our measurements of the conductance of a nanoparticle array device controlled bythe oxidation state of individual molecules pave the way towards using nanoparticlearrays as an interface to monitor chemical processes. The high surface area of thenanoparticles in the arrays make them interesting as sensing platforms. Having a largesurface to volume ratio in a detector increases the odds of capturing the small amountof molecules present in a dilute solution. The next step towards using the nanoparticlearrays as transport sensitive chemical sensors concern performing electrical transportmeasurements in a solution. The challenges that need to be over come to accomplishthis concern decreasing leakage current from the electrodes through the solution andincreasing the device sensitivity to interactions between the molecules in the solutionand the nanoparticle arrays. The ultimate limit would be, for example, to detect theoxidation of a single redox–active molecule in the array.

A part of the solution to the challenges stated above was be to be able to makethe nanoparticle arrays as small as one likes and have good control over the electrodegeometry. To reduce the leakage current between the electrodes their area should bekept as small as possible. To work at low voltages, in order to prevent electrochemicalbreakdown of the solvent, the distance between the electrodes needs to be small.To be sensitive to the oxidation of a single redox–active molecule the arrays shouldideally be one dimensional. Thus, controlling the geometry of the devices preciselyis important.

One way to utilise the mechanical stability of molecular junctions on a substrateand avoid the problems of the disorder in the nanoparticle arrays is to contact a singlenanoparticle with two electrodes. In a recent collaboration with Hassan Jafri andKlaus Leifer at the Department of Engineering Sciences, Electron Microscopy andNanoengineering at Uppsala University, we measured the transport through devicescomprising of 5 nm diameter nanoparticles trapped in 20 nm wide nanogaps. Thenanogaps were made by cutting through a thin gold wire, patterned with e–beamlithography, by a focused ion beam (FIB). The results of these measurements are

7.1. Outlook 79

presented in Appendix A.A reoccurring question in molecular electronics is how to independently control the

mechanical and electrical coupling of a molecule to the electrodes. One idea proposedto answer the question is to prepare ligands which can wrap around a small goldnanoparticle and give good mechanical stability. The electrical coupling between themolecule and the nanoparticle can then be addressed separately. In this way it ispossible to synthesise dumbbell molecules, comprising of two nanoparticles and themolecule bridging them [26]. Nanogap structures might be useful to contact suchdumbbell molecules.

In order to know the electronic transport paths in our arrays detailed KPFMmeasurements are needed. The collaboration with Thilo Glatzel and Marcin Kisiel isstill running and we hope that in the future we can directly measure the asymmetryof the coupling between the electrodes and the nanoparticle array and see how thecurrent paths branch through the array.

The possibilities are endless and our imagination is the only limitation, besides thelimitation of time.

80 Conclusions and outlook

Bibliography

[1] Agrait, N., Untiedt, C., Rubiobollinger, G., and Vieira, S. (2002). Electrontransport and phonons in atomic wires. Chemical Physics, 281(2-3):231–234.

[2] Amman, M., Wilkins, R., Jacob, E. B., Maker, P. D., and Jaklevic, R. C. (1991).Analytic solution for the current-voltage characteristic of two mesoscopic tunneljunctions coupled in series. Physical Review B, 43(1):1146–1149.

[3] Andreu, R. (2001). Electronic absorption spectra of closed and open-shell tetrathiafulvalenes: the first time-dependent density-functional study.Tetrahedron, 57(37):7883–7892.

[4] Arroyo, C. R., Frederiksen, T., Bollinger, G. R., Vélez, M., Arnau, A.,Portal, D. S., and Agrait, N. (2010). Characterization of single-moleculepentanedithiol junctions by inelastic electron tunneling spectroscopy and first-principles calculations. Physical Review B, 81(7):075405.

[5] Aviram, A. and Ratner, M. A. (1974). Molecular rectifiers. Chemical PhysicsLetters, 29(2):277–283.

[6] Beebe, J. M., Moore, H. J., Lee, T. R., and Kushmerick, J. G. (2007). VibronicCoupling in Semifluorinated Alkanethiol Junctions: Implications for SelectionRules in Inelastic Electron Tunneling Spectroscopy. Nano Letters, 7(5):1364–1368.

[7] Beloborodov, I. S., Lopatin, A. V., Vinokur, V. M., and Efetov, K. B. (2007).Granular electronic systems. Reviews of Modern Physics, 79(2):469–518.

[8] Bendikov, M., Wudl, F., and Perepichka, D. F. (2004). Tetrathiafulvalenes,Oligoacenenes, and Their Buckminsterfullerene Derivatives: The Brick andMortar of Organic Electronics. Chemical Reviews, 104(11):4891–4946.

81

82 Bibliography

[9] Bernard, L., Kamdzhilov, Y., Calame, M., Van der Molen, S. J., Liao, J.,and Schönenberger, C. (2007). Spectroscopy of Molecular Junction NetworksObtained by Place Exchange in 2D Nanoparticle Arrays. J. Phys. Chem. C,111(50):18445–18450.

[10] Blom, T., Welch, K., Strømme, M., Coronel, E., and Leifer, K. (2007).Fabrication and characterization of highly reproducible, high resistance nanogapsmade by focused ion beam milling. Nanotechnology, 18(28):285301.

[11] Bryant, M. A. and Pemberton, J. E. (1991). Surface Raman scattering of self-assembled monolayers formed from 1-alkanethiols: behavior of films at goldand comparison to films at silver. Journal of the American Chemical Society,113(22):8284–8293.

[12] Castiglioni, C., Gussoni, M., and Zerbi, G. (1991). Charge mobility in sigma-bonded molecules: The infrared spectrum of polymethylene chains in the solidand liquid phases. The Journal of Chemical Physics, 95(10):7144–7149.

[13] Datta, S., Tian, W., Hong, S., Reifenberger, R., Henderson, J. I., and Kubiak,C. P. (1997). Current-Voltage Characteristics of Self-Assembled Monolayers byScanning Tunneling Microscopy. Physical Review Letters, 79(13):2530–2533.

[14] de la Vega, Rodero, A. M., Agrait, N., and Yeyati, A. L. (2006). Universalfeatures of electron–phonon interactions in atomic wires. Physical Review B,73(7):075428.

[15] Djukic, D., Thygesen, K. S., Untiedt, C., Smit, R. H. M., Jacobsen, K. W., andvan Ruitenbeek, J. M. (2005). Stretching dependence of the vibration modes of asingle–molecule Pt–h_2–Pt bridge. Physical Review B, 71(16):161402.

[16] Donkers, R. L., Song, Y., and Murray, R. W. (2004). Substituent Effects onthe Exchange Dynamics of Ligands on 1.6 nm Diameter Gold Nanoparticles.Langmuir, 20(11):4703–4707.

[17] Elteto, K., Lin, X. M., and Jaeger, H. M. (2005). Electronic transport in quasi-one-dimensional arrays of gold nanocrystals. Physical Review B, 71(20):205412.

[18] Frederiksen, T., Lorente, N., Paulsson, M., and Brandbyge, M. (2007). Fromtunneling to contact: Inelastic signals in an atomic gold junction from firstprinciples. Physical Review B, 75(23):235441.

[19] Gagliardi, A., Solomon, G. C., Pecchia, A., Frauenheim, T., Di Carlo, A., Hush,N. S., and Reimers, J. R. (2007). A priori method for propensity rules for inelasticelectron tunneling spectroscopy of single-molecule conduction. Physical ReviewB, 75(17):174306.

Bibliography 83

[20] Galperin, M., Nitzan, A., Ratner, M. A., and Stewart, D. R. (2005). MolecularTransport Junctions: Asymmetry in Inelastic Tunneling Processes. The Journal ofPhysical Chemistry B, 109(17):8519–8522.

[21] Galperin, M., Ratner, M. A., and Nitzan, A. (2004). Inelastic electron tunnelingspectroscopy in molecular junctions: Peaks and dips. The Journal of ChemicalPhysics, 121(23):11965–11979.

[22] Gimzewski, J. K. and Möller, R. (1987). Transition from the tunneling regimeto point contact studied using scanning tunneling microscopy. Physical Review B,36(2):1284–1287.

[23] Grüter, L., Cheng, F., Heikkilä, T. T., Teresa González, M., Diederich, F.,Schönenberger, C., and Calame, M. (2005). Resonant tunnelling through a C60molecular junction in a liquid environment. Nanotechnology, 16(10):2143–2148.

[24] Hanna, A. E. and Tinkham, M. (1991). Variation of the Coulomb staircasein a two-junction system by fractional electron charge. Physical Review B,44(11):5919–5922.

[25] Heeger, A. J. (2001). Nobel Lecture: Semiconducting and metallic polymers:The fourth generation of polymeric materials. Reviews of Modern Physics,73(3):681–700.

[26] Hermes, J. P., Sander, F., Peterle, T., and Mayor, M. (2011). Nanoparticlesto Hybrid Organic-Inorganic Superstructures. CHIMIA International Journal forChemistry, 65(4):219–222.

[27] Hihath, J., Arroyo, C. R., Rubio-Bollinger, G., Tao, N., and Agrait, N.(2008). Study of Electron–Phonon Interactions in a Single Molecule CovalentlyConnected to Two Electrodes. Nano Letters, 8(6):1673–1678.

[28] Hihath, J., Bruot, C., and Tao, N. (2010). Electron–Phonon Interactions inSingle Octanedithiol Molecular Junctions. ACS Nano, 4(7):3823–3830.

[29] Hostetler, M. J., Templeton, A. C., and Murray, R. W. (1999). Dynamicsof Place-Exchange Reactions on Monolayer-Protected Gold Cluster Molecules.Langmuir, 15(11):3782–3789.

[30] Jafri, S. H. M, Blom, T., Wallner, A., Welch, K., Strømme, M., Ottosson, H., andLeifer, K. (2010). Control of junction resistances in molecular electronic devicesfabricated by FIB. Microelectronic Engineering.

[31] Jafri, S. H. M., Blom, T., Leifer, K., Strømme, M., Löfås, H., Grigoriev, A.,Ahuja, R., and Welch, K. (2010). Assessment of a nanoparticle bridge platformfor molecular electronics measurements. Nanotechnology, 21(43):435204.

84 Bibliography

[32] Jaklevic, R. C. and Lambe, J. (1966). Molecular Vibration Spectra by ElectronTunneling. Physical Review Letters, 17(22):1139–1140.

[33] Jan van der Molen, S. and Liljeroth, P. (2010). Charge transport throughmolecular switches. Journal of Physics: Condensed Matter, 22(13):133001.

[34] Joseph, Y., Besnard, I., Rosenberger, M., Guse, B., Nothofer, H. G., Wessels,J. M., Wild, U., Knop-Gericke, A., Su, D., Schlogl, R., Yasuda, A., andVossmeyer, T. (2003). Self-Assembled Gold Nanoparticle/Alkanedithiol Films:Preparation, Electron Microscopy, XPS-Analysis, Charge Transport, and Vapor-Sensing Properties. J. Phys. Chem. B, 107(30):7406–7413.

[35] Kardar, M., Parisi, G., and Zhang, Y. C. (1986). Dynamic Scaling of GrowingInterfaces. Physical Review Letters, 56(9):889–892.

[36] Kato, H. S., Noh, J., Hara, M., and Kawai, M. (2002). An HREELS Studyof Alkanethiol Self-Assembled Monolayers on Au(111). The Journal of PhysicalChemistry B, 106(37):9655–9658.

[37] Klein, J., Léger, A., Belin, M., Défourneau, D., and Sangster, M. J. L. (1973).Inelastic-Electron-Tunneling Spectroscopy of Metal-Insulator-Metal Junctions.Physical Review B, 7(6):2336–2348.

[38] Kushmerick, J. G., Lazorcik, J., Patterson, C. H., Shashidhar, R., Seferos, D. S.,and Bazan, G. C. (2004). Vibronic Contributions to Charge Transport AcrossMolecular Junctions. Nano Letters, 4(4):639–642.

[39] Lambe, J. and Jaklevic, R. C. (1968). Molecular Vibration Spectra by InelasticElectron Tunneling. Physical Review Online Archive (Prola), 165(3):821–832.

[40] Lambe, J. and Jaklevic, R. C. (1969). Charge-Quantization Studies Using aTunnel Capacitor. Physical Review Letters, 22(25):1371–1375.

[41] Lauhon, L. J. and Ho, W. (2001). Effects of temperature and other experimentalvariables on single molecule vibrational spectroscopy with the scanning tunnelingmicroscope. Review of Scientific Instruments, 72(1):216–223.

[42] Liao, J., Agustsson, J. S., Wu, S., Schönenberger, C., Calame, M., Leroux, Y.,Mayor, M., Jeannin, O., Ran, Y.-F., Liu, S.-X., and Decurtins, S. (2010). CyclicConductance Switching in Networks of Redox–Active Molecular Junctions. NanoLetters, 10(3):759–764.

[43] Liao, J., Bernard, L., Langer, M., Schönenberger, C., and Calame, M.(2006). Reversible Formation of Molecular Junctions in 2D Nanoparticle Arrays.Advanced Materials, 18(18):2444–2447.

Bibliography 85

[44] Liao, J., Mangold, M. A., Grunder, S., Mayor, M., Schönenberger, C., andCalame, M. (2008). Interlinking Au nanoparticles in 2D arrays via conjugateddithiolated molecules. New J. Phys., 10(6):065019.

[45] Liao, J., Zhou, Y., Huang, C., Wang, Y., and Peng, L. (2011). Fabrication,Transfer, and Transport Properties of Monolayered Freestanding NanoparticleSheets. Small, 7(5):583–587.

[46] Mantooth, B. A. and Weiss, P. S. (2003). Fabrication, assembly, andcharacterization of molecular electronic components. Proceedings of the IEEE,91(11):1785–1802.

[47] Middleton, A. A. and Wingreen, N. S. (1993). Collective transport in arrays ofsmall metallic dots. Physical Review Letters, 71(19):3198–3201.

[48] Muller, C., Van Ruitenbeek, J., and Dejongh, L. (1992). Experimentalobservation of the transition from weak link to tunnel junction. Physica C:Superconductivity, 191(3-4):485–504.

[49] Nonnenmacher, M., O’Boyle, M. P., and Wickramasinghe, H. K. (1991). Kelvinprobe force microscopy. Applied Physics Letters, 58(25):2921–2923.

[50] Okabayashi, N. and Komeda, T. (2009). Inelastic electron tunnelingspectroscopy with a dilution refrigerator based scanning tunneling microscope.Measurement Science and Technology, 20(9):095602.

[51] Okabayashi, N., Paulsson, M., Ueba, H., Konda, Y., and Komeda, T.(2010). Inelastic Tunneling Spectroscopy of Alkanethiol Molecules: High-Resolution Spectroscopy and Theoretical Simulations. Physical Review Letters,104(7):077801.

[52] Parthasarathy, R., Lin, X. M., Elteto, K., Rosenbaum, T. F., and Jaeger,H. M. (2004). Percolating through Networks of Random Thresholds: FiniteTemperature Electron Tunneling in Metal Nanocrystal Arrays. Physical ReviewLetters, 92(7):076801.

[53] Paulsson, M., Frederiksen, T., and Brandbyge, M. (2005). Modeling inelasticphonon scattering in atomic- and molecular-wire junctions. Physical Review B,72(20):201101.

[54] Paulsson, M., Frederiksen, T., and Brandbyge, M. (2006). Inelastic Transportthrough Molecules: Comparing First–Principles Calculations to Experiments.Nano Letters, 6(2):258–262.

86 Bibliography

[55] Paulsson, M., Frederiksen, T., Ueba, H., Lorente, N., and Brandbyge, M.(2008). Unified Description of Inelastic Propensity Rules for Electron Transportthrough Nanoscale Junctions. Physical Review Letters, 100(22):226604.

[56] Pekola, J. P., Hirvi, K. P., Kauppinen, J. P., and Paalanen, M. A. (1994).Thermometry by Arrays of Tunnel Junctions. Physical Review Letters,73(21):2903–2906.

[57] Rahimi, M. and Hegg, M. (2009). Probing charge transport in single-moleculebreak junctions using inelastic tunneling. Physical Review B, 79(8):081404.

[58] Rahimi, M. and Troisi, A. (2009). Probing local electric field andconformational switching in single-molecule break junctions. Physical ReviewB, 79(11):113413.

[59] Reed, M. (2008). Inelastic electron tunneling spectroscopy. Materials Today,11(11):46–50.

[60] Salomon, A., Cahen, D., Lindsay, S., Tomfohr, J., Engelkes, V. B., and Frisbie,C. D. (2003). Comparison of Electronic Transport Measurements on OrganicMolecules. Adv. Mater., 15(22):1881–1890.

[61] Santhanam, V. and Andres, R. P. (2004). Microcontact Printing of UniformNanoparticle Arrays. Nano Letters, 4(1):41–44.

[62] Santhanam, V., Liu, J., Agarwal, R., and Andres, R. P. (2003). Self-Assemblyof Uniform Monolayer Arrays of Nanoparticles. Langmuir, 19(19):7881–7887.

[63] Song, H., Kim, Y., Jeong, H., Reed, M. A., and Lee, T. (2010). CoherentTunneling Transport in Molecular Junctions. The Journal of Physical ChemistryC, 114(48):20431–20435.

[64] Stipe, B. C., Rezaei, M. A., and Ho, W. (1998). Single-Molecule VibrationalSpectroscopy and Microscopy. Science, 280(5370):1732–1735.

[65] Tal, O., Krieger, M., Leerink, B., and van Ruitenbeek, J. M. (2008). Electron-Vibration Interaction in Single-Molecule Junctions: From Contact to TunnelingRegimes. Physical Review Letters, 100(19):196804.

[66] Taniguchi, M., Tsutsui, M., Yokota, K., and Kawai, T. (2009). Inelasticelectron tunneling spectroscopy of single-molecule junctions using a mechanicallycontrollable break junction. Nanotechnology, 20(43):434008.

Bibliography 87

[67] Tran, T. B., Beloborodov, I. S., Hu, J., Lin, X. M., Rosenbaum, T. F.,and Jaeger, H. M. (2008). Sequential tunneling and inelastic cotunneling innanoparticle arrays. Physical Review B (Condensed Matter and MaterialsPhysics), 78(7):075437.

[68] Troisi, A. and Ratner, M. A. (2006). Molecular Transport Junctions: PropensityRules for Inelastic Electron Tunneling Spectra. Nano Letters, 6(8):1784–1788.

[69] Troisi, A. and Ratner, M. A. (2006). Propensity rules for inelastic electrontunneling spectroscopy of single-molecule transport junctions. The Journal ofChemical Physics, 125(21):214709.

[70] Trouwborst, M. L., Huisman, E. H., van der Molen, S. J., and van Wees, B. J.(2009). Bistable hysteresis and resistance switching in hydrogen-gold junctions.Physical Review B, 80(8):081407.

[71] Tsutsui, G., Huang, S., Sakaue, H., Shingubara, S., and Takahagi, T. (2001).Well-size-controlled Colloidal Gold Nanoparticles Dispersed in Organic Solvents.Jan. J. Appl. Phys, 40:346–349.

[72] Ueba, H., MII, T, and Tikhodeev, S. (2007). Theory of inelastic tunnelingspectroscopy of a single molecule – Competition between elastic and inelasticcurrent. Surface Science, 601(22):5220–5225.

[73] van der Molen, S. J., Liao, J., Kudernac, T., Agustsson, J. S., Bernard, L.,Calame, M., van Wees, B. J., Feringa, B. L., and Schönenberger, C. (2009). Light–Controlled Conductance Switching of Ordered Metal–Molecule–Metal Devices.Nano Letters, 9(1):76–80.

[74] Šuvakov, M. and Tadic, B. (2010). Modeling collective charge transport innanoparticle assemblies. Journal of Physics: Condensed Matter, 22(16):163201.

[75] Wang, C., Batsanov, A. S., and Bryce, M. R. (2004). Electrochromictetrathiafulvalene derivatives functionalised with 2,5-diaryl-1,3,4-oxadiazolechromophores. Chem. Commun., (5):578–579.

[76] Wang, C., Palsson, L. O., Batsanov, A. S., and Bryce, M. R. (2006).Molecular Wires Comprising π-Extended Ethynyl- and Butadiynyl-2,5-Diphenyl-1,3,4-Oxadiazole Derivatives: Synthesis, Redox, Structural, and OptoelectronicProperties. J. Am. Chem. Soc., 128(11):3789–3799.

[77] Wu, S., Gonzalez, M. T., Huber, R., Grunder, S., Mayor, M., Schonenberger, C.,and Calame, M. (2008). Molecular junctions based on aromatic coupling. NatureNanotechnology, 3(9):569–574.

88 Bibliography

[78] Zabet-Khosousi, A. and Dhirani, A.-A. (2008). Charge Transport inNanoparticle Assemblies. Chemical Reviews, 108(10):4072–4124.

[79] Zimmerman, D. T., Weimer, M. B., and Agnolet, G. (1999). An adjustableoxide-free tunnel junction for vibrational spectroscopy of molecules. AppliedPhysics Letters, 75(16):2500–2502.

Appendix AMeasurements on nanoparticles trapped innanogaps

A.1 Introduction

We had the opportunity to collaborate with Hassan Jafri and Klaus Leifer at theDepartment of Engineering Sciences, Electron Microscopy and Nanoengineering atUppsala University. They make devices of nanoparticles trapped in nanogaps[10, 31,30]. These devices are interesting for us since they contain far fewer nanoparticlesthan our current devices. The first results of our measurements on their devices areshown in this appendix.

A priory these devices were promising for IETS measurements since they haveonly a few, ∼ 3 − 5, nanoparticles in series between the electrodes. As we realisedduring our measurements, although promising, these devices had their drawbacks.As seen in Figure A.1 some of the devices had very asymmetric IV responses. Theseasymmetries arise from the size distribution of the nanoparticles in the gaps. Theyhave a diameter of 5 ± 1 nm. The charging energies of individual nanoparticle rangefrom Ec = 100 meV for an individual 6 nm diameter nanoparticle to Ec = 150 meVfor 4 nm diameter nanoparticle. The voltages needed to overcome Coulomb blockadein these nanoparticles are VCB = 200 mV and VCB = 300 mV for the 6 and 4 nmdiameter nanoparticles, respectively. The nanoparticles are trapped in the nanogapsusing delectrophoretic trapping. The coupling between the electrodes and clusters ofnanoparticles is probably asymmetric, although it is hard to estimate the asymmetry.Furthermore, the conducting paths through the trapped clusters are also ill defined.In the case of these devices the conductance takes place through a disordered threedimensional cluster or even several such clusters.

89

90 Measurements on nanoparticles trapped in nanogaps

−2.0 −1.5 −1.0 −0.5 0 0.5 1.0 1.5 2.0−500

−250

0

250

500

Vbias [V]

I[pA]

Polarity 1 10 mVPolarity 2 20 mV

Figure A.1: An IV measurement of a device with nanoparticles trapped in a nanogap. The two curves in thefigure were measured with two different polarities. The reversal of the asymmetry along with thereversal of the polarity of the sample indicate that the transport through the device is asymmetric.The voltage and current are not scaled to account for the number of junctions in the device sincewe do not know how many nanoparticles take part in the transport.

−2.0 −1.5 −1.0 −0.5 0 0.5 1.0 1.5 2.01

3

5

7

Vbias [V]

Re(dI/dV)[A

/V]


Figure A.2: dI/dV measurements of the same device as in Figure A.1. The dI/dV has many features, butsince we do not know the sizes and the number of nanoparticles in the gap it is impossible toassign the features to specific processes.

A.1. Introduction 91

−2.0 −1.5 −1.0 −0.5 0 0.5 1.0 1.5 2.0−8

−4

0

4

8

Vbias [V]

Im(d

2I/dV

2)[A

/V

2 bias]


Figure A.3: The d2I/dV2 measurements of the same device as in Figure A.1. The asymmetry of the deviceis clearly visible.

From these first measurements we have learned that the nanogaps fabricated in theGroup of Klaus Leifer offer an interesting platform for transport measurements onmolecular junctions on a substrate. At the moment it is difficult to interpret the dataobtained from these devices due to the fact that the size of the nanoparticles trappedin the them are small compared to the width of the nanogaps and there is a relativelylarge size distribution of the nanoparticles. Because of this it is impossible to predicthow the current will flow through the nanoparticle clusters trapped in these devices.As discussed in Chapter 5 features in the IETS below the threshold for conduction,Vth, are masked by Coulomb blockade. The small nanoparticles trapped in these gapshave a threshold voltage of Vth ≈ 200 − 300 mV. As discussed in Chapter 6 manyphonon modes active in transport have energies between 50− 300 meV. These modescannot be observed if the threshold voltage to overcome Coulomb blockade is as highas it is in these devices.

A solution to this problem would be to trap nanoparticles of the same diameteror larger than the nanogap width. If this were done it would be possible to createdouble junction devices and thus certainly only having one or two molecular junctionsin series. Nanoparticles with a diameter of ∼ 20 nm should be large enough toaccomplish this. These nanoparticles would have charging energy of Ec = 30 meVand a threshold voltage to overcome Coulomb blockade of Vth = 60 mV. Thus,opening up the possibility to measure phonon energies above ∼ 60 meV.

92 Measurements on nanoparticles trapped in nanogaps

Appendix BMeasurements on nanoparticles usingKPFM

It is of interest to measure the which conducting paths are most favourable inthe nanoparticle arrays. Until now, we do not have detailed knowledge of howthe nanoparticle array contacts the electrodes or how grain boundaries or defectsinfluence the transport in the arrays. One way of answering these questions is byKelvin probe force measurements (KPFM) [49]. Using KPFM it is possible to mapout the current paths in the devices. In a collaboration with Thilo Glatzel and MarcinKisiel, in the group of Ernst Meyer at Basel University, have started looking at thearrays with a KPFM.

So far we have not been able to measure the details of the transport using themethod. This is due to the fact that the measurement is apparently quite difficult andrequires the use of a well tuned instruments. Preliminary measurements show that itis possible to correlate a height profile measured with AFM to the contact potentialmeasured with the KPFM. Figure B.1 shows an example of an AFM and a KPFMmeasurement on one device. The dark area on the right side of the figures is thesubstrate and the bright area on the left side is the nanoparticle array.

Since these measurements were made the KPFM has been optimised and now itshould be possible to make more detailed measurements. Three is mutual interest incontinuing the collaboration and we hope to have nice measurements in the future.

93

94 Measurements on nanoparticles using KPFM

Figure B.1: AFM and KPFM measurements on a nanoparticle array. There figures show that it is possibleto distinguish between the nanoparticle array and the substrate using AFM and KPFM. The darkarea on the right side of the figures is the substrate and the bright area on the left side is thenanoparticle array.

Appendix CImages of suspended nanoparticle arrays

In a collaboration with Susanne Baumann, a student at the Basel University, we triedfabricating freely suspended nanoparticle arrays. Two methods were tried. Onefocused on fabricating small nanoparticle arrays as described in Chapter 4. As alast step, after stamping the nanoparticles on the devices, the SiO2 was etched awayusing buffered HF. After the HF etching the SiO2 supporting the nanoparticles shouldbe gone and the nanoparticle array free standing. On occasion, devices containingsuspended nanoparticle arrays were observed by SEM. Figure C.1 shows a devicewhere a nanoparticle array is suspended between two electrodes.

Figure C.1: An SEM image of a suspended nanoparticle array.

Looking closely at the SEM images and looking at several devices it becameapparent that the nanoparticle array was not truly free–standing but supported by

95

96 Images of suspended nanoparticle arrays

an unknown film. Figure C.2 shows how the nanoparticles are supported by a grayfilm.

Figure C.2: An SEM image of a suspended nanoparticle array. The nanoparticles bridging the electrodes aresupported by an unknown gray film.

Most devices looked like the one shown in Figure C.3. Although beautiful, theyare useless for scientific measurements of transport.

Figure C.3: An SEM image of a suspended nanoparticle array. After etching beautiful nanoparticleassemblies decorate the sample.

A different approach to fabricate free–standing nanoparticle arrays was imple-mented by Susanne Baumann. She made free–standing nanoparticle arrays which

97

spanned the openings of TEM grids. Figure C.4 shows an optical image ofnanoparticle arrays spanning an opening in a TEM grid. Depositing these suspendednanoparticle arrays was problematic. Liao et al. [45] make free–standing nanoparticlearrays in a similar fashion and use high pressure air to transfer the nanoparticle arrayfrom the TEM grid to the substrate. Unfortunately we did not think of this.

Figure C.4: An optical image of a suspended nanoparticle array in a TEM grid.

98 Images of suspended nanoparticle arrays

Appendix DProtocol for nanoparticle array fabrication

All chemicals used in the synthesis and suspension of the nanoparticles were boughtat Sigma–Aldrich and used as received unless otherwise stated. The di–ionised waterhad a resistivity greater than 13 MΩ–cm.

D.1 Au nanoparticle Synthesis

Colloidal gold particles, with a diameter of 10 nm, were formed by the reduction ofgold(III) chloride hydrate (HAuCl4·4H2O, ACS reagent ≥ 49% Au basis) by sodiumcitrate tribasic dihydrate (C6H5O9Na3·2H2O, for molecular biology ≥ 99.5%) andtannic acid (C76H52O46, ACS reagent)[71].

D.1.1 Solutions used

The solutions used are:

• 1 ml 1% (w/v) gold(III) chloride hydrate (HAuCl4·4H2O) in DI–H2O.

• 4 ml 1% (w/v) sodium citrate tribasic dihydrate (C6H5O9Na3·2H2O) in DI–H2O.

• 80 μl 1% (w/v) tannic acid (C76H52O46) in DI–H2O.

D.1.2 Protocol

• Use two beakers (a) 150 ml and (b) 25 ml.

99

100 Protocol for nanoparticle array fabrication

• Clean beakers thoroughly using water and soap. Rinse using DI-H2O.

• Turn hotplate to 80◦C.

• In beaker (a) put:

– 1 ml gold(III) chloride hydrate (HAuCl4·4H2O).

– 79 ml DI-H2O.

– Place magnetic stirrer in beaker and turn on stirring.

– Cover beaker.

– Heat to 80◦C on hotplate (10-15 min).

• In beaker (b) put:

– 4 ml sodium citrate tribasic dihydrate (C6H5O9Na3·2H2O), for 10 nmgold colloids.

– 80 μl tannic acid (C76H52O46).

– Add water to fill 20 ml.

– Cover beaker.

– Heat to 80◦C on hotplate (10-15 min).

• Turn hotplate to 250◦C, wait 5 min.

• Quickly pour the contents of beaker (b) into beaker (a).

• The solution will turn purple.

• Wait until the solution color changes to red.

• When solution is red wait 10 more minutes.

• Cool solution to room temperature by placing the beaker in ice water. Stircontinuously.

D.1.3 Extracting gold colloids and covering with a ligand

The gold colloids need to be extracted from the aqueous solution. This is done usinga high–speed centrifuge, Heraeus Biofuge Pico.

• Place the colloid solution into test tubes. 1 ml into each eppendorf.

• Place eppendorfs symmetrically into centrifuge.

• Run centrifuge at 13 krpm for 45 min.

D.1. Au nanoparticle Synthesis 101

• Clean a 20 ml bottle with ethanol (CH3CH2OH, ACS reagent, absolute alcohol,without additive ≥ 99.8%).

• With a pipette carefully remove water from the colloids.

• Mix colloids and the remaining water.

• Infuse ethanol in each eppendorf.

• Mix with shaker.

• Transfer the ethanol–colloid solutions from all eppendorfs into the 20 ml bottle.

• Put the solution in an ultrasonic bath for 10 min (sweep) at a temperature below30◦C.

• Add 200 μl of the desired covering molecule to the bottle. 1–Octanethiol(CH3(CH2)7SH,≥ 98.5%, distilled before usage) or 1–Dodecanethiol (CH3(CH2)11SH,≥ 98%).

• Fill the bottle with ethanol.

• The color changes as the molecules cover the gold particles.

• Wait 2–3 days for the molecules to form a ordered layer on the gold

D.1.4 Washing the colloids

After the colloids have settled in the bottom of the small bottle the excess ligands canbe removed and the colloids washed in Ethanol before they can be used as an ink forstamping.

After this process the solution can be stored for up to a week before it is ruined.

• With a pipette remove excess solution from colloids.

• Infuse new ethanol.

• Wait until colloids precipitate, about 1 hr.

• Remove all ethanol, very carefully.

• Infuse 4 ml chloroform (CHCl3, ACS spectroscopy grade ≥ 99.8%, 0.5–1.0%Ethanol).

• To disperse colloids put the bottle in ultrasonic bath at room temperature for10 min.

• The solution turns red when ready.


D.2 Colloid density

The number of 10 nm diameter colloids resulting from the reduction of 1 ml 1% (w/v)HAuCl4·4H2O can be calculated as:

1100

g = HAuCl4 · 4H2O (D.1)

HAuCl4 · 4H2O = 411.8 Amu (D.2)

Au = 197 Amu (D.3)

The density of gold is:

DAu = 19300kgm3 (D.4)

DAu = 1.93 × 10−20 gnm3 (D.5)

The volume of a 10 nm diameter colloid is:

VColloid =43πr3 (D.6)

VColloid = 524 nm3 (D.7)

The mass of one colloid is then:

MColloid = VColloid × DAu (D.8)

MColloid = 1 × 10−17 g (D.9)

The total mass of Au in the solution is:

MAuinsol =197 Amu

411.8 Amu× 1

100g (D.10)

MAuinsol = 4.8 × 10−3 g (D.11)

And the total number of colloids in the solution is then:

#Colinsol =4.8 × 10−3 g1 × 10−17 g

(D.12)

#Colinsol = 4.8 × 1014 Colloids (D.13)

The colloid density is

4.8 × 1014 Colloids80 ml

= 6 × 1012 Colloids/ml (D.14)

D.3. Preparation of masters for PDMS stamps using UV lithography 103

The colloid density in the chloroform solution is

6 × 1012 Colloids/ml × 10 ml4 ml

= 1.5 × 1013 Colloids/ml (D.15)

D.3 Preparation of masters for PDMS stamps using UVlithography

The masters for the PDMS stamps were made by patterning SU–8 on a SiO2 substrate.

• Spin:

– 500 rpm - ramp time 5 s - for 10 s

– 4000 rpm - ramp time 9 s - for 30s

• Bake: 1 min @ 95o C

• Expose: 2.5 s (i-line), 6s Hard Contact (1.2-1.3 Bar) (33mW/cm2*s)

• Bake IMMEDIATELY after exposure: 1 min @ 95oC.

• Develop: SU-8 developer for 1 min

• Clean and dry in IPA

• Hard bake: 10min @ 200oC

D.4 PDMS

Stamps are made from PDMS molded on the SU8 masters fabricated using UVlithography. The PDMS, SYLGARD R© 184 SILICONE ELASTOMER KIT, is usedas bought from Dow Corning.

• In a small vile pour 15 ml of base and 2 ml of the curing agent.

• Stir well, until a uniform distribution of small bubbles has formed.

• In a petri dish pour the PDMS over the substrates.

• Wait until no bubbles are close to the substrates, at least 30 min.

• Heat an oven to 60◦C.

• Bake PDMS for 90 minutes.

• Let PDMS cool down and carefully pull it out of the petri dish.


• Using a sharp knife peel off the thin PDMS layer on the bottom of the masters.

• Cut slightly along the edges of the masters and carefully remove them from thePDMS.

• After you remove the masters from the PDMS there should be no PDMS lefton the top surface of the Si masters. The transferred pattern is visible in thePDMS.

• Use a razor blade to cut out each PDMS stamp.

• Clean stamps in ethanol ultrasonic bath for 5 min.

D.5 Transferring patterns using PDMS stamps

Using a colloid solution in chloroform as ink and PDMS stamps self assembled arrayscan be transferred to a substrate [62, 61]

Use a petri dish with three glass slides stacked in the bottom on two sides. Beforeplacing the Teflon ring in the dish, clean the Teflon ring thoroughly using soap andwater then rinse with DI–H2O.

Place the Teflon ring on the glass slide stacks and carefully infuse 29 ml DI-H2Ointo the dish outside of the Teflon ring. The colloid solution can be suspended on thewater surface for the self assembled monolayer (SAM) to form.

• Turn on airflow in the fume hood, to help solvent to evaporate.

• Use a regular pipette to put 350 ∼ 400 μl of solution into a small vial.

• Using a glass pipette empty the vial and place the solution in the centre of theTeflon ring.

• Wait 10-15 min until all the solvent has evaporated.

• Carefully bring PDMS stamp to touch the surface. Hold the stamp at thesurface for 10 sec.

• Tilt the stamp to break contact with the surface and remove it.

• Dry off all excess water on the stamp.

• Place the stamp on the petri dish.

• By dropping, place a substrate on top of the stamp.

• Wait 10 sec. and remove the substrate from the stamp.

D.6. Fabrication of small nanoparticle arrays 105

D.6 Fabrication of small nanoparticle arrays

D.6.1 Substrate cleaning and preparation of PMMA

• Use highly p– doped Si substrate, resistivity ∼ 10 μΩ–cm dopant boron.Thermal oxide thickness 400nm.

• Clean substrate in a ultrasonic bath first with acetone (C3H6O, for analysisfrom Merck Chemicals), then isopropanol (C3H8O, for analysis from MerckChemicals) for 10min each solvent. Dry sample with nitrogen gas.

• Clean substrate in UV ozone for 10 min (Jelight Company model 42).

• Spin on a 120nm thick layer of PMMA–MA 33% (AR–P 671.09 950K fromALLRESIST) at 2000 rpm, ramp 4sek, and duration 40sek.

• Bake PMMA–MA on a hot plate at 200◦C for 10min.

• Spin 600-700nm thick PMMA (AR–P 671.09 950K from ALLRESIST, di-luted) at 4000rpm, ramp 4sek, and duration 40sek.

• Bake on a hotplate at 180◦C for 10min.

D.6.2 E–beam writing and development

Structures written in Zeiss Supra 40 SEM.

• Acceleration voltage: 30 kV

• Working distance: 9 mm

• Area dose: 290 μAs/cm2.

• Aperture for large structures: 120 μm.

• Write field size: 1000 μm.

• Dose factor: 1.2

• Aperture for small structure: 10 μm.

• Write field size: 100 μm.

• Dose factor: 1.2

Develop in 1:3 4–methyl–2–pentanone(MIBK, C6H12O):isopropanol for 90 sec-onds. Clean in oxygen plasma using a Oxygen Plasmalab80 Plus reactive ion etcher(RIE) from Oxford:


• Background pressure: 5 × 10−5 mTorr

• Working pressure: 250 mTorr

• O2 flow: 16 sccm

• Power: 30 W

• Time: 20 sec

D.6.3 Metal evaporation

Meta evaporation is performed in a Sharon Vacuum evaporator. The Ti and Aufilms are evaporated with electron beam evaporation, while the Cr film is evaporatedthermally. Figure D.1 shows how the metal electrodes are evaporated on the substrate.The goal of the angular evaporation is to fabricate a relatively smooth height gradientfrom the metal electrodes to the bare SiO2 separating them. The process yields metalelectrodes approaching the SiO2 in three steps each having a smaller height thanan individual nanoparticle diameter. This will prevent the nanoparticle array frombraking when deposited on top of the structure. The structure is composed of a Tiadhesion layer, an Au conducting layer, and a Cr etching mask.

After the metal evaporation liftoff is performed in heated acetone. After liftoffthe samples are rinsed in isopropanol and UV ozone for 10min. The liftoff andisopropanol rinse are performed in an ultrasonic bath at 20% power. Fresh layersof PMMA–MA/PMMA are spun on using the process describe in section D.6.1.Small bridges, bridging the metal electrodes, are written. This is done using thesame parameters as for the small structures in Sub.Sec D.6.2.

After e–beam writing the substrate is developed as before in 1:3 MIBK:Isopropanolfor 90sec. After developing the sample is further cleaned in O2 plasma as above.

A 45nm Cr etching mask is evaporated onto the substrate. The evaporation isperformed at room temperature and under 0◦ angle. After evaporation liftoff isperformed as described above.

D.6.4 SiO2 etching

To fabricate small structures of nanoparticle arrays one needs to pattern the SiO2

substrate, since the PDMS is too flexible to support these small structures. Using Cras an etching mask, the SiO2 can be etched away leaving a raised structure with metalcontacts on top separated by exposed SiO2. The SiO2 etching is performed usingreactive ion etching (RIE). This etching method is more anisotropic than hydrofluoricacid (HF) etching. During RIE etching of the SiO2 using CHF3 as an etching gas afluorocarbon polymer is deposited on the side walls of the structure. This polymer isalmost impossible to remove, but the remaining polymer can be kept to a minimum

D.6. Fabrication of small nanoparticle arrays 107

Figure D.1: The evaporation process for the large contact pads. At the top the structure of the electrodes isshown from above as written by the e–beam. The green areas represent the exposed SiO2 andthe white areas represent the PMMA. The horizontal line represents a cut through the structure.The bottom figure shows a side view of the metallic layers as deposited onto the substrate. Theview is along the line cut shown in the top figure. The α values represent the angle chosenon the evaporator sample holder and Θ the relative angle between the normal of the substrateand the incoming metal atoms. The numbers followed by a metal and a thickness (i.e. 1) Ti3nm) represent the order of the evaporated layers, the evaporated metal and the thickness of theevaporated metal. The coverage of the last 20nm Cr metal layer is not depicted in the figure.

in two ways. During CHF3 etching small amount of O2 is mixed with the CHF3.After etching with CHF3 the deposited polymer can be oxidised in a O2 plasma andremoved using heated Acetone in an ultrasonic bath. The normal etching process isdescribed below in table D.1.

Pressure [mTorr] O2 flow [sccm] CHF3 flow [sccm] power [W] time [m:s]

25 16 0 100 2:0025 2 40 100 20:00

250 16 0 100 2:00

Table D.1: The RIE etching process. This process will etch ∼200nm of SiO2.


D.6.5 Cr etching

The Cr etching mask is removed using a solution of ceric ammonium nitrate((NH4)2Ce(NO3)6, CAN) in Di–H2O and Acetic acid (CH3COOH):

• 10ml Di–H2O

• 2g CAN

• 260μl Acetic acid

The etching rate of the solution is ∼ 3 nm/sec if the sample is dipped in an onlyslightly agitated. To fully remove the Cr the etching is performed in a ultrasonic bathat 20% power for 3min.

D.6.6 Stamping of Au nanoparticle arrays

When the raised structures have been prepared the nanoparticle arrays are stampedon top of them using a PDMS stamp with no pattern.

D.7 Molecular place exchange

For 2 mg OPE dithiol (426.55 g/mole) in 3 ml THF:

• Weigh molecule and add in a flask

• Infuse THF to the flask

• Bubble with Ar for 1–2 minutes

• Add 20 μL ammonium hydroxide Sigma Aldrich is 17837-100ML

• Bubble with Ar for 1–2 minutes

• Drop sample in the flask. Structures facing down.

• Store under Ar atmosphere over night

• Remove sample rinse twice with THF

• Dry sample

Appendix EElectrical characterisation of the dip–stick

E.1 Frequency response of 10 GΩ resistor in the dip–stick

The frequency response of a 10 GΩ resistor in the dip–stick at room temperature isshown in figure E.1. The blue marks are the measured points and the blue dotted linea guide to the eye. The green line is a model of the differential conductance assuminga parallel connection of a resistor R = 11 GΩ and a capacitor C = 2.1 pF

dIdV

=1R+ iωC (E.1)

The chip carrier is connected to a break out box with a flat ribbon cable of twistedpair wires. During the measurement wire 6 and 16 were used. They belong to the thirdand eighth twisted pairs respectively. To reduce the capacitive cross talk betweenthem all the unused wires were grounded.

Using equation E.1 one can get the differential conductance of the equivalentcircuit measured, assuming the circuit consists of the resistor being measured inparallel with a stray capacitance to ground. From the real part of the dI/dVmeasurement one gets the value of the resistor R = 1/Re{dI/dV} = 11 GΩ andfrom the imaginary part of the signal one gets the value of the stray capacitance toground C = Im{dI/dV}/(ω) = 2.1 pF.

The d2I/dV2 measurements show only noise when the resistor is measured. This isexpected since the impedance of the equivalent circuit should not depend on voltage.

109

110 Electrical characterisation of the dip–stick

102

103

104

10−9

10−8

10−7

Amp(dI/dV)[S]

102

103

104−90

−45

0

45

90

Angle(dI/dV)[D

eg]

F [Hz]

Figure E.1: The frequency response of a 10 GΩ resistor in the dip–stick. The blue marks are the measureddata point and the blue dotted line a guide for the eye. The green line is a model of the differentialconductance of the system with C = 2 pF and R = 10 GΩ. The bandwidth of the IV converter isreached around 5 kHz.

E.1. Frequency response of 10 GΩ resistor in the dip–stick 111

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

−200

−100

0

100

200

Vbias [V]

I[pA]

−2 −1 0 1 288.0

88.2

88.4

88.6

88.8

89.0

Vbias [V]

Re(dI/dV)[pS]

−2 −1 0 1 2974.7

974.8

974.9

975.0

975.1

Vbias [V]

Im(dI/dV)[pS]

−2 −1 0 1 2−10

−5

0

5

10

Vbias [V]

Im(d

2I/dV

2)[×

10−12A/V

2]

Figure E.2: IV , dI/dV , and d2I/dV2 measurement of a 10 GΩ resistor in the dip–stick. The dI/dV andd2I/dV2 are measured at a frequency of 73 Hz. From the IV and the real part of the dI/dV onecan see that the resistance of the resistor is R = 11 GΩ. From the imaginary part of the dI/dVone can calculate the capacitance C = 2.1 pF.

112 Electrical characterisation of the dip–stick

Appendix FTaylor expansion of the current measured

F.1 Details of the Taylor expansion of the current measurements

The current flowing in the device is comprised of an ac part and a dc part and can beexpressed by a Taylor series as

I(Vdc + Vac sin(ωt)) = I(Vdc) +dI(Vdc)

dVVac sin(ωt) +

12

d2I(Vdc)dV2 V2

ac sin2(ωt)

+d2I(Vdc)

dV2

V2ac

4+ · · · (F.1)

sin2(ωt) =1 − cos(2ωt)

2(F.2)

I(Vdc + Vac sin(ωt)) = I(Vdc) +dI(Vdc)

dVVac sin(ωt) +

14

d2I(Vdc)dV2 V2

ac cos(2ωt + π)

+d2I(Vdc)

dV2

V2ac

2+ · · · (F.3)

Assuming a circuit comprised of a parallel connection of a resistor R and a capacitorC the dI(Vdc)/dV in (F.3) can be written as:

dI(Vdc)dV

=1R+C

ddt

(F.4)

113

114 Taylor expansion of the current measured

inserting (F.4) into (F.3) gives

I(Vdc + Vac sin(ωt)) = I(Vdc) +(

1R+C

ddt

)Vac sin(ωt)

+14

ddV

(1R+C

ddt

)V2

ac cos(2ωt + π)

+d

dV

(1R+C

ddt

)V2

ac

2+ · · · (F.5)

The phase of the current can be represented in the complex plane by defining the inphase part of the signal, ∝ sin(ωt), as being on the real axis and the out of plane partof the signal, ∝ cos(ωt), as being imaginary. The second term in (F.5) can then berepresented as (

1R+C

ddt

)Vac sin(ωt) =

1R

Vac sin(ωt) + ωCVac cos(ωt)

Re{(

1R+C

ddt

)Vac sin(ωt)

}=

1R

Vac

Im{(

1R+C

ddt

)Vac sin(ωt)

}= ωCVac (F.6)

Assuming that the resistor and capacitor are voltage controlled the third term in (F.5)can then be represented as

14

ddV

(1

R(Vdc)+C(Vdc)

ddt

)V2

ac cos(2ωt + π) =d

dV

(1

4R(Vdc)V2

ac cos(2ωt + π)

+14ωC(Vdc)V2

ac sin(2ωt))

Re{

14

ddV

(1

R(Vdc)+C(Vdc)

ddt

)V2

ac cos(2ωt + π)}=

ddV

14ωC(Vdc)V2

ac

Im{

14

ddV

(1

R(Vdc)+C(Vdc)

ddt

)V2

ac cos(2ωt + π)}=

ddV

14R(Vdc)

V2ac (F.7)

As Equations F.6 and F.7 show the resistance R and capacitance C can be measureddirectly by measuring the real, in phase, and imaginary, out of phase, components ofthe ac current, respectively. The voltage derivative of the resistance and capacitancecan also be measured directly by measuring the imaginary and real parts of the secondharmonic of the ac current, respectively.

Appendix GError calculations

G.1 Calculation of the broadening in the Coulomb blockadeinduced feature due to disorder in the nanoparticle array

Nanoparticle capacitance in a nanoparicle array:

C = 4πε0εrR(R + s)

R

δC = 4πε0εr

√(2R + s

sδR

)2

+

(2R2

s2 δs)2

(G.1)

where ε0 is the permittivity of vacuum, εr the dielectric constant, R the nanoparticleradius, and s the interparticle distance. The error in the capacitance δC is due to theerror in the nanoparticle radius and the interparticle distance.

Charging energy.

Ec =e2

2C

δEc =e2

2C2 δC (G.2)

where e is the elementary charge of an electron.

115

116 Error calculations

Voltage to over come Coulomb blockade:

VCB =2Ec

e

δVCB =2δEc

e(G.3)

Reduction factor of threshold voltage due to temperature:

P(T ) =4.8kBTρcEc

δP(T ) =2 · 4.8kBTρcE2

cδEc (G.4)

where kB is the Boltzmann constant, T the temperature, and ρc = 2 sin(18/π) thepercolation threshold in a hexagonally closed array.

Threshold voltage:

Vth = VCB(1 − P(T ))

δVth =

√((1 − P(T ))δVCB)2 + (VCBδP(T ))2 (G.5)

Threshold voltage per molecular junction:

Vth j =Vth

N

δVth j =

√(δVth

N

)2

+

(Vth

N2 δN)2

(G.6)

where N is the number of nanoparticles spanning the gap between the electrodes.The number of nanoparticles spanning the gap between the electrodes:

N =L

2R + s

δN =

√(δL

2R + s

)2

+

(L

(2R + s)2δs

)2

+

(L

(2R + s)2 2δR)2

(G.7)

G.2 Calculation of the broadening in the Coulomb blockadeinduced feature due to charge disorder in the nanoparticlearray

Assuming the model shown in Figure 5.1 with C1 = C2 and the charge on thenanoparticle Q = 0. The change in the energy of the nanoparticle when a single

G.2. Calculation of the broadening in the Coulomb blockade induced feature due to chargedisorder in the nanoparticle array 117

charge is added to it is:

ΔU± =(Q ± e)2

2C− Q2

2C(G.8)

where e is the charge of an electron and C = C1 + C2 is the capacitance of thenanoparticle. Now the error in the energy U due to charge disorder δQ and disorderin the nanoparticle capacitance δC, from Equation G.1 is:

δΔU± =

√(2eδQ2C

)2

+

(e2δC2C2

)2

(G.9)

where δ denotes the error of δU±. The error of δU± is carried to the change in energywhen an electron tunnels onto or off the nanoparticle. The change in energy is givenby:

ΔE±1 = ΔU± ∓ eC2

CΣVb

ΔE±2 = ΔU± ± eC1

CΣVb (G.10)

as given by Equation 5.4. The error of ΔE±j , j = 1, 2, due to the error in ΔU± is:

δΔE±j =

√(δΔU±)2 +

√2( eVbδC

C

)2

(G.11)

where Vb is the bias applied to the junction. Combining Equations 5.1, 5.3, 5.4, and5.7 the threshold voltage for conductance in the presence of Coulomb blockade in asymmetric double junction is found as in Equation 5.8, but with errors added

− (Ec ± δΔE±j ) ≤ 12

eVb ≤ (Ec ± δΔE±j ) (G.12)

which gives the voltage needed to over come Coulomb blockade with errors due tocharge disorder and errors in the nanoparticle capacitance

|VCB| = 2EC/e

δ|VCB| = 2δΔE±j /e (G.13)

The error of |VCB| is carried forward to the threshold voltage as shown in EquationG.6.

118 Error calculations

G.3 Calculation of the broadening of peaks beyond the thresholdvoltage due to variations in the interparticle separation

The nanoparticles in the array are capacitively coupled. We make the assumptionthat that the voltage drop between two neighbouring nanoparticles will depend on thecapacitance between the nanoparticles[2, 24, 47]. In the terms of the double junctiontunnelling model the voltage is found as in Equation 5.5:

Vj =C1C2

C jCΣVb (G.14)

where C j is the capacitance of the individual junction, CΣ = C1 + C2 is the sumof the capacitances of the junctions, Vb is the applied bias voltage, the number ofnanoparticles in series bridging the electrodes. Using Equations G.14 and G.1 thebroadening in the voltage between the nanoparticles can be calculated as:

δVi j =1√1

δCC

(G.15)

Appendix HLiterature values of phonon modes inmolecules

H.1 Phonon modes in CH3(CH2)8SH and CH3(CH2)7SHmolecules on an Au surface.

119

120 Literature values of phonon modes in molecules

ModeWavenumber[cm−1]

Energy[meV] Molecule Method Reference

Au–S stretch 225 28 CH3(CH2)7SH HREELS [36]Au–S stretch 255 32 CH3(CH2)7SH HREELS [36]SCC deformCCC deform

385 48 CH3(CH2)7SH HREELS [36]

ν(C–S)G 641 79 CH3(CH2)8SH RAMAN [11]ν(C–S)T 706 88 CH3(CH2)8SH RAMAN [11]CH2 rock 715 89 CH3(CH2)7SH HREELS [36]CH2 rocking 720 89 CH3(CH2)5CH3 IR [12]CH2 rocking 766 95 CH3(CH2)5CH3 IR [12]CH3 rock 915 113 CH3(CH2)7SH HREELS [36]CH2 rocking 925 115 CH3(CH2)5CH3 IR [12]C–C stretch 1050 130 CH3(CH2)7SH HREELS [36]νa(C–C)T 1064 132 CH3(CH2)8SH RAMAN [11]νs(C–C)T 1120 139 CH3(CH2)8SH RAMAN [11]CH3 rock 1190 148 CH3(CH2)7SH HREELS [36]CH2 wagging 1230 152 CH3(CH2)5CH3 IR [12]CH2 twist 1265 157 CH3(CH2)7SH HREELS [36]CH2 wagging 1283 159 CH3(CH2)5CH3 IR [12]CH2 wagging 1330 165 CH3(CH2)5CH3 IR [12]CH3 s–deform 1380 171 CH3(CH2)7SH HREELS [36]CH3 d–deformCH2 scissors

1455 180 CH3(CH2)7SH HREELS [36]

νs(CH2) 2854 354 CH3(CH2)8SH RAMAN [11]C–H stretch 2860 355 CH3(CH2)7SH HREELS [36]νs(CH2) 2880 357 CH3(CH2)8SH RAMAN [11]νs(CH2) 2907 360 CH3(CH2)8SH RAMAN [11]C–H stretch 2925 363 CH3(CH2)7SH HREELS [36]νs(CH3FR) 2936 364 CH3(CH2)8SH RAMAN [11]νs(CH3) 2967 368 CH3(CH2)8SH RAMAN [11]

Table H.1: A summary of phonon modes in alkane thiols. The molecules are adsorbed onto Au surfaces andthe phonon modes are investigated by Raman spectroscopy, high–resolution electron–energy–lossspectroscopy (HREELS), and infra red (IR) spectroscopy.

Publication list

Publications in journals

• In–situ resistivity measurements during growth of ultra-thin Cr0.7Mo0.3

K. B. Gylfason, A. S. Ingason, J. S. Agustsson, S. Olafsson, K. Johnsen and J.T. Gudmundsson, Thin Solid Films 515 (2006) 583-586

• A magnetron sputtering system for the preparation of patterned thin films andin–situ thin film electrical resistance measurementsU. B. Arnalds, J. S. Agustsson, A. S. Ingason, A.-K. Eriksson, K. B. Gylfason,J. T. Gudmundsson, and S. Olafsson, Review of Scientific Instruments 78 (10)(2007) 103901

• Growth, coalesnce and electrical resistivity of thin Pt films grown by dcmagnetron sputtering on SiOJ. S. Agustsson, U. B. Arnalds, A. S. Ingason, K. B. Gylfason, K. Johnsen,S. Olafsson and J. T. Gudmundsson, Applied Surface Science 254(22) (2008)7356-7360

• In–situ electrical characterization of ultrathin TiN films grown by reactive dcmagnetron sputtering on SiOA. S. Ingason, F. Magnus, J. S. Agustsson, S. Olafsson, and J. T. Gudmunds-son, Thin Solid Films, 517 (24) (2009) 6731-6736

• Light–Controlled Conductance Switching of Ordered Metal–Molecule–MetalDevicesSense Jan van der Molen, Jianhui Liao, Tibor Kudernac, Jon S. Agustsson,Laetitia Bernard, Michel Calame, Bart J. van Wees, Ben L. Feringa andChristian Scöhnenberger, Nano Letters, 2009, 9 (1), pp 76-80

• Cyclic Conductance Switching in Networks of Redox–Active Molecular Junc-tionsJianhui Liao, Jon S. Agustsson, Songmei Wu, Christian Schönenberger, Michel

121

122 Publication list

Calame, Yann Leroux, Marcel Mayor, Olivier Jeannin, Ying-Fen Ran, Shi-XiaLiu and Silvio Decurtins, Nano Letters, 2010, 10 (3), p 759-764

Poseter contributions

• Ultra–thin Lattice Matched CrxMo1−x /MgO MultilayersK. B.Gylfason, J. S.Ágústsson, S. Ólafsson, I. Meyvantsson, K. Johnsen andJ. T. Guðmundsson, Poster presented at the 51st American Vacuum SocietySymposium, Anaheim, California, November 16. 2004 (J. T. Guðmundssonpresented)

• In–situ Resistivitymeasurements during growth of ultrathin CrxMo1−x

K. B.Gylfason, Á. S. Ingason, J. S. Ágústsson, S. Ólafsson, K. Johnsen, and J.T. Guðmundsson, Poster presented at the 13th International Congress on ThinFilms, Stockholm, Sweden, June 19 - 23, 2005 (K. B. Gylfason presented)

• Electrical charectization of MgO thin films grown by reactive magnetronsputteringJ. T. Guðmundsson, J. S. Ágústsson, K. B. Gylfason, S. Ólafsson, and K.Johnsen, Poster presented at the 13th International Congress on Thin Films,Stockholm, Sweden, June 19 - 23, 2005 (J. S. Ágústsson presented)

• In–situ Resistivity measurements during growth of ultra thin CrxMo1−x

K. B. Gylfason, Á. S. Ingason, J. S. Ágústsson, S. Ólafsson, K. Johnsen,and J. T. Guðmundsson, Poster presented at the Natural Science Symposium,Reykjavík, Iceland, March 3 - 4, 2006 (K. B. Gylfason presented)

• Rafeiginleikar þunnra MgO húðaJ. S. Ágústsson, K. B.Gylfason, B. V. Ágústsson, S. Ólafsson, K. Johnsen,and J. T. Guðmundsson, Poster presented at the Natural Science Symposium,Reykjavík, Iceland, March 3 - 4, 2006 (J. S. Ágústsson presented)

• Hydrogen uptake in MgO thin films grown by reactive magnetron sputteringJ. S. Ágústsson, B. V. Ágústsson, A. K. Eriksson, K. B. Gylfason, S. Ólafsson,K. Johnsen, and J. T. Guðmundsson, Poster presented at the 53st AmericanVacuum Society Symposium, San Francisco, California, November 14. 2006(J. S. Ágústsson presented)

• Cyclic conductance switching in networks of redox–active molecular junctionsDepartment of Physics, University of Basel, Switzerland Jianhui Liao, Jon S.Agustsson, Songmei Wu, Christian Schönenberger, and Michel Calame, Posterpresented at Swiss nano, 2009 (J. Liao presented)

123

• Molecular devices based on arrays of gold nanoparticlesJon S. Agustsson, Haichao Huang, Jianhui Liao, Christian Schönenberger, andMichel Calame, Poster presented at the International Conference on MolecularElectronics, Emmetten, Switzerland, January 5–9. 2010 (J. S. Agustssonpresented)

• Molecular devices based on arrays of gold nanoparticlesJon S. Agustsson, Claire Barrett, Jianhui Liao, Christian Schönenberger, andMichel Calame, Poster presented for the NCCR review panel, 2010 (J. S.Agustsson presented)

Oral presentations

• Reactive sputtering of oxide thin filmsNatural Science Symposium, Reykjavík, Iceland, March 3 - 4, 2006

• Molecules as active components in devices based on networks of molecularjunctions.Workshop on molecular electronics in Bern, May 2009

• Molecules as active components in devices based on networks of molecularjunctionsMulhouse, France, 2009

• Molecules as active components in devices based on networks of molecularjunctions.FUNMOLS project meeting in Copenhagen, September 2009

• Molecules as active components in devices based on networks of molecularjunctions.10th European Conference on Molecular Electronics in Copenhagen, Septem-ber 2009

• Nanoparticle arraysFunMol project meeting in Basel, October 2009

124 Publication list

Curriculum vitae

Jón Skírnir ÁgústssonBorn October 12th 1978 in Reykjavík, Iceland

Education

• August 1994 – June 1999The Commercial College of Iceland (Verzlunarskóli Íslands), Reykjavík,Iceland

• August 1996 – June 1997Woodland Hills High School, Pittsburgh, Pennsylvania, USAExchange student

• Agust 1999 – January 2004Bachelor of Science in Electrical Engineering at the University of Iceland

• January 2004 – June 2004Student exchange at the University of California Santa Barbara, Santa Barbara,California, USA

• January 2004 – June 2005Master of Science in Electrical Engineering at the University of IcelandMasters thesis under the super vision of Dr. Jón Tómas Guðmundsson:"Electrical characterization of MgO thin films grown by reactive magnetronsputtering"

• October 2007 – June 2011 Ph.D. thesis at the University of Basel under thesupervision of Prof. Christian Schönenberger: "Arrays of gold nanoparticlesas a platform for molecular electronics"

125

126 Curriculum vitae

Professional positions

• Summers 2000 – 2003IT department at Reykjavík Energy, Reykjavík, Iceland

• Winters 2001 – 2003Math teacher at the Commercial College of Iceland (Verzlunarskóli Íslands),Reykjavík, Iceland

• Winter 2002 – 2003Natural science teacher at Hamraskóli, Reykjavík, Iceland

• June 2005 – September 2007Electrical Engineer at Mentis Cura ehf, Reykjavík, Iceland

Acknowledgements

The three and a half years I have spent in Basel have been very rewarding. I havegrown academically, personally, and even financially, relative to many of my owncountrymen.

I am thankful that Christian Schönenberger took me into his group. He has a talentfor creating an particularly friendly and comfortable work environment. It is rareto find a person who can so nicely balance support, friendliness, and yet questionevery measurement and protocol. I remember meetings where you criticised all mywork, but in a way that was constructive and inspired by helpfulness. Those werehard meetings, but also the ones where I came out motivated to answer the questionsI could not answer in the meeting.

Of all the people I met during my study Michel Calame is the one who has inspiredme the most. You has taught me about science and life. You showed me how toappreciate the best Switzerland has to offer: The food, the wine, and the mountains.Michel you have a special talent of holding my hand and kicking my ass at the sametime.

Jianhui Liao was the one who introduced me to the secret of the nanoparticlearrays. He has to be the most patient man I have met. Although we are two verydifferent people, I think we made a good team and I would have loved to work onthe suspended arrays with you. I realised how patient you were when I had to teachothers to make the arrays. I did not need a lot of patience when I taught Claire Barrettto make the nanoparticle arrays. She picked up on the protocol quickly after sherealised to mix the solutions with water and not ethanol. Claire, thank you for thesupport and all the talks in the last year of my thesis.

Thanks to Aidan Quinn and Sense Jan van der Molen for taking the time andrefereeing my thesis defence.

The people who make up the group have made the stay here fun and easy. I havemet many interesting and fun people who have helped me develop in many ways. Iam truly thankful for the great companionship I have experienced in the group: Allthe trips to the climbing halls with Andreas Kleine, Jens Schindele, Jan Brunner,Cornelia Nef, and Lukas Hofstetter; The avalanche and mountaineering discussions

127

128 Acknowledgements

with Markus Weiss, and Toni Frölich; The ski waxing tips from Romain Maurand;The skiing trips with Hagen Aurich, Jelena Trbovic and, Samuel d’Hollosy; Thesocial events by Alexey Tarasov, Oren "Funny man" Knopfmacher, Mathias Wipf,and Julia Samm; I have had interesting discussions on many topics from ballroomdancing to optimising Matlab code and implementing Matlab code on the poultrycomputer with; Andreas Baumgartner, Matthias Bräuninger, Alexander Eichler, andWangyang Fu; And enjoyed the silence with Stefan Nau. During the writing ofmy thesis I was fortunate to have two quiet office mates. David Just and PeterRickhaus. I often had helpful discussions with the "old" molecular people RomanHuber, Songmei Wu, Teresa Gonzales, and Zheng–Ming Wu. To the former andcurrent members of the group I give my regards.

Without two Icelanders I probably would not have made it to Basel. SigurðurErlingsson, Siggi, gave me the idea of applying in the group and Gunnar Gunnarssonbuilt a good reputation for Icelanders in the group.

When I sit here and write this thesis I have come to realise how far we havedeveloped the nanoparticle arrays during my stay in the group. When I say we Irefer not only to the people in the group of Christian Schönenberger, but the newergenerations of people working on the nanoparticle arrays started here in the group.We have surely branched out and looked into different aspects of the structure:Markus Mangold and Alexander Holleitner with the optical measurements, ConstantGuédon and Sense Jan van der Molen with the interparticle spacing, and last but notleast Jianhui Liao with the suspended nanoparticle arrays. It has been a pleasure tomeet, work, and discuss with all of these people and some of the most innovative ideason the development of the nanoparticle arrays were probably born during our latenight discussions in the conference organised by Michel and Christian in Emmetten.

I had the pleasure to work with several people on collaborations. I had fun with theCdSe nanoparticles prepared by Yunfei Zhou and Michael Krüger. I was even invitedby Alexander Holleitner to visit his lab in München. I spent two weeks with HassanJafri measuring his nanogap samples. In house I also made contact to Thilo Glatzeland Marcin Kisiel who can measure my nanoparticle arrays with a KPFM. I had theopportunity to work with a project student, Susanne Baumann did nice work on thefree standing nanoparticle arrays.

I cannot write the acknowledgements without mentioning the great staff at thePhysics Institute. Without them I probably would not have lasted longer than a fewweeks in Basel. Barbara Kammermann and Astrid Kalt have taken care of everythingI have brought to them, big and small. It has been a great pleasure to work withDaniel Sacker keeping the Balzers evaporator alive. The mechanical workshop andelectrical workshops have made our life much easier. Their high quality work andendless patience has been invaluable to our work.

My family in Iceland have had their influence on my and I would probably not bethe man I am today with out them. They have supported me as much as they can fromafar.

129

My girlfriend María has made my stay here in Switzerland so enjoyable. I amreally thankful that she decided to move to Basel with me and partake in this wholeadventure. Together we have discovered new ways to enjoy the life in Switzerlandand how useful skis are in that respect.

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